effect of pressure-sensitive demand on surge analysis m · pdf fileeffect of...

100 APRIL 2009 | JOURNAL AWWA • 101:4 | PEER-REVIEWED | JUNG ET AL

Effect of pressure-sensitive demand on surge analysis

Traditional water distribution models solve the network problem by considering instantaneous

demands lumped as nodal outflows. Such demand-driven analysis assumes that demands are

independent of pressures and can be met under all operating conditions. Under transient

conditions, however, the resulting positive- or negative-pressure surges can drastically alter

the local pressures and affect the demand magnitude that can be extracted. A pressure-

sensitive demand representation is needed to assess the effect of pressure changes and

produce more accurate transient results. A comparative study of demand formulations for surge

analysis showed that the pressure-insensitive demand assumption is intrinsically inaccurate

and tends to overdesign surge protection devices. This overdesign results in unnecessary

additional costs but does not necessarily ensure greater safety. The authors conclude that a

pressure-sensitive demand formulation should be used for surge analysis to adequately

evaluate both system performance and the ultimate cost of system protection.

BY BONG SEOG JUNG,

PAUL F. BOULOS,

AND DON J. WOOD

eeting the goals of the Safe Drinking Water Act demands a multi-barrier approach that ensures adequate protection of source waterfrom contamination, effective treatment of raw water, and safe dis-tribution of this treated water to consumers’ taps. The latter objec-tive requires, among other precautionary measures, protecting the dis-

tribution system from intrusion of contaminants as a result of objectionablepressure transients. Given that all pipeline systems leak and hydraulic transientsoccur continuously in most distribution systems, low-pressure transients canrepresent a significant risk of drawing untreated and possibly hazardous waterinto a pipeline system (Karney, 2003).

BACKGROUNDTransient pressures and their effects. Intrusion refers to the flow of nonpotable

water into drinking water mains through leaks and other openings resultingfrom low transient or negative pressures (Boulos et al, 2006; NRC, 2006).Depending on the size of the leaks, the volume of intrusion can range from a fewgallons to hundreds of gallons (LeChevallier et al, 2002; Funk et al, 1999;LeChevallier, 1999). Transient regimes are inevitable. Any disturbance in thewater caused during a change in hydraulic state (typically from one steady or equi-librium condition to another) can initiate a sequence of transient pressures in thewater distribution system. At some point in time, all systems will be started up,

M

2009 © American Water Works Association

JUNG ET AL | 101:4 • JOURNAL AWWA | PEER-REVIEWED | APRIL 2009 101

switched off, or undergo rapid flow changes and willlikely experience the effects of human errors, equipmentbreakdowns, earthquakes, or other risky disturbances.Transient pressure can cause breaches in distribution sys-tem integrity that have significant impli-cations for water quality and public health.Transients can generate high intensities offluid shear and may cause resuspension ofsettled particles as well as biofilm detach-ment. Moreover, a low-pressure transient(such as one arising from a power failureor a broken water main) has the potentialto cause the intrusion of contaminatedgroundwater into a pipe at a leaky jointor break. This risk is especially significantfor systems with pipes below the water table. Dissolvedair (gas) can also be released from the water whenever thelocal pressure drops considerably, and this may promotethe corrosion of steel and iron sections with subsequentrust formation and pipe damage.

If not properly designed and maintained, even somecommon strategies for protection from transients (suchas relief valves or air chambers) may permit pathogens orother contaminants to find a “back door” route into thepotable water distribution system. In the event of a sig-nificant intrusion of pathogens (e.g., as a result of a bro-ken water main), the level of chlorine residual normallysustained in drinking water distribution systems may beinsufficient to disinfect the contaminated water, which canlead to damaging health effects. A recent case study inKenya showed that in the event of a 0.1% raw sewagecontamination, the available residual chlorine within thedistribution network would not be sufficient to safe-guard the water (Ndambuki, 2006). Although not allintrusions are caused by pressure transients, excellentreviews of the effects of pressure transients on distribu-tion system water quality degradation are available inthe literature (Boulos et al, 2006; NRC, 2006; Lansey &Boulos, 2005; Wood et al, 2005a, 2005b; Gullick et al,2004; McInnis, 2004; Karim et al, 2003; LeChevallier etal, 2003; Kirmeyer et al, 2001; Funk et al, 1999;LeChevallier, 1999).

Transient analysis. Hydraulic transient analysis providesthe most effective and viable means of identifying weakspots, predicting potentially negative effects of hydraulictransients under various worst-case scenarios, and evalu-ating how transients may be eliminated or controlled. Tran-sient flow in pipes is described by nonlinear hyperbolicpartial differential equations of continuity and momen-tum principles. A direct solution of these equations is notpossible because of the presence of nonlinearity and thecomplexity associated with the pipe network configura-tion and associated boundary conditions. Various numer-ical methods have been developed for analyzing transientflow in pressurized conduits, including a linear analyzingsolution scheme (an approximate analytical solution by

linearizing the friction term in the governing transient flowequations), implicit method (finite difference procedure),finite element method, and graphical water-hammerapproach (Wylie & Streeter, 1993; Chaudhry, 1987). How-

ever, application of these methods has been limited becauseof their insufficient accuracy and inherent difficulty in solv-ing complex multiloop networks.

In general, the most popular and viable methods forsolving hydraulic transient problems are the method ofcharacteristics and the wave characteristic method (Bou-los et al, 2006; Wood et al, 2005a, 2005b). The methodof characteristics transforms the governing transient flowequations into ordinary equations. These ordinary differ-ential equations are then integrated to obtain a finite dif-ference representation of the pressure head and flow. Thewave characteristic method solves the transient flow prob-lem in an event-oriented system simulation environment.In this environment, the pressure wave propagation processis driven by the distribution system activities. Otherresearchers have made a detailed comparison of the accu-racy and computational time requirements for the twomethods (Wood et al, 2005a; 2005b). They found thatboth methods produced virtually identical results but thatthe wave characteristic method was more efficient in termsof both time and memory for analyzing large water dis-tribution systems. Ghidaoui and colleagues provided ageneral history and introduction to water-hammer phe-nomena, a compendium of key developments and litera-ture reference, and an updated view of the current state ofthe art, with respect to both theoretical advances of the lastdecade and modeling practices (Ghidaoui et al, 2005).

Strategies for controlling transients. Several techniquesare available for suppressing and controlling hydraulictransients in water distribution systems (Boulos et al,2006, 2005; Wood et al, 2005a). These strategies rangefrom system modification and operational considerationsto installation of surge-control devices. Operational con-siderations focus on the root causes of flow changes, suchas adjusting valve or pump operations. They may includeprolonging valve opening and closing times, using a two-stage valve closure and opening, or increasing pump iner-tia by adding a flywheel to prolong pump stoppage andstartup times. System modifications can include rein-forcing pipes (i.e., increasing the pressure rating), rerout-ing and changing the network topology, using larger-

Transient pressure can cause breaches in distributionsystem integrity that have significant implications for waterquality and public health.



diameter pipes, or installing different pipe material (Jung& Karney, 2004). The final surge-protection strategy,most commonly considered in pipeline systems, involvesadding surge-control devices. The general principles ofthese devices are to store water or otherwise delay thechange of flow or to discharge water from the piping sys-tem so that rapid or extreme fluctuations in the flowregime are minimized. Devices such as pressure-reliefvalves, surge-anticipation valves, surge vessels, surgetanks, and pump bypass lines are commonly used to con-trol maximum pressures. Minimum pressures can be con-trolled by adding surge vessels, surge tanks, air-release/vac-uum valves, or pump-bypass lines. Overviews of thevarious common surge-protection devices and their func-tions can be found elsewhere (Boulos et al, 2006, 2005;Wood et al, 2005a; Thorley, 1991).

In general, a combination of these devices may proveto be the most desirable and most economical strategy.Other research provided a detailed transient flow chart tothe selection of components for surge control and sup-pression in water distribution systems and concluded thata transient analysis should always be carried out to deter-mine the effect of each proposed strategy on the resultingsystem performance (Boulos et al, 2005). Such anapproach is a fundamental part of rational networkdesign. A more recent study showed that only system-atic and informed transient analysis can be expected toresolve complex transient characterizations and ade-quately protect a distribution system from the vagaries andchallenges of rapid transients (Jung et al, 2007a).

WATER DEMAND MODELSIn conventional water distribution transient models,

it is presumed that the nodal demand is independent ofpressure (demand-driven analysis) and is always satisfied

under all operating conditions (including zero or nega-tive pressure). In the actual system, the demand wouldnot be met (the demand becomes zero when the pressuredrops to zero or less than zero). Various techniques formodeling nodal demand as a function of nodal pres-sures (generally termed head-driven analyses) have beenproposed (Ang & Jowitt, 2006; Gupta & Bhave, 1996;Jowitt & Xu, 1993). Of the several methods reviewed byGupta and Bhave (1996), the method using the para-bolic head-discharge relationship (no flow at minimumhead to required flow at desired head) yielded the bestprediction of network performance. These researchersalso detailed the basic differences between the variousdemand modeling approaches, including the parabolichead-discharge and the standard orifice-based methods(Gupta & Bhave, 1996). However, the applications ofthese methods were restricted to steady network analy-sis under normal conditions, and only a few methodshave been implemented in transient analysis. McInnisand Karney (1995) introduced a distributed pipe fluxdemand model and compared it with both constant(pressure-insensitive) and orifice-based (pressure-sensi-tive) demand models. These three demand models werealso compared with field test data using a network tran-sient model. More recently, Karney and Filion (2003)assessed the primary energy-dissipation mechanisms,including orifice-type leaks, commonly found in pipelinesystems under water-hammer conditions.

Pressure-sensitive demand can be simulated with emit-ters that discharge the flow through a nozzle or orificeto the atmosphere. The flow rate through the emittervaries as a function of the pressure available at the junc-tion node and can be expressed as

Q � Cd AH� � C�d Ap� � Cemit p� (1)

in which Q is the flow rate from the emitter; H and p arethe total head and pressure at that emitter, respectively;Cd and C�d are discharge coefficients for the total headand pressure, respectively; Cemit is the emitter coeffi-cient; and � is a pressure exponent, usually taken as0.5. The value of the emitter coefficient is calculated asthe flow through the device at a 1-psi pressure dropwith units of gpm/psi0.5. Using Eq 1, the emitter is usedto simulate the effect of the pressure-sensitive demand.A typical pressure-sensitive demand curve for anextended period simulation is shown in Figure 1. Start-ing with no flow at zero pressure, the nodal demandincreases with increasing pressure and stabilizes to therequired flow when the desirable pressure is reached,typically 20 psi.

The constant demand formulation could benefit thesteady-state model (especially at large demand points)and could provide a conservative measure in transientpipeline systems. However, pressure transients can dras-tically alter the local pressures, which in turn can sig-

FIGURE 1 Design of pressure-sensitive demand in the extended period simulation

Qrequired

Qrequired

Qavailable

Prequired

Dem

and

Pressure

P—pressure, Q—flow rate



nificantly affect the magnitude of nodal demands thatcan be extracted. The fixed demand ignores the pres-sure-sensitive characteristic implicit in actual transientpipeline systems, which can lead to poor design, unreli-able protection, and/or unsafe operation of these sys-tems. Therefore a pressure-sensitive demand represen-tation is needed to assess the effect of pressure changes

on the supplied flows and produce more accurate tran-sient modeling results. This article describes a compar-ative study of demand formulation for surge analysis.The study encompassed both pressure-sensitive and pres-sure-insensitive demands. Both demand analysis meth-ods are demonstrated using two pipeline system, exam-ples. The first example is for a small pipeline system,and the second is for an actual water distribution net-work system. Results showed that the assumption ofpressure-insensitive demand exaggerates a surge wave inthe distribution system, which could lead to overdesignof selected surge-protection devices and added costs. Inlight of these findings, the authors concluded that apressure-sensitive demand formulation should alwaysbe used for surge analysis in order to adequately evalu-ate both system performance and the ultimate cost of sys-tem strengthening.

WATER DEMAND: ASSUMPTION AND APPROXIMATIONWater demand classifications. Water demand is the

main driving force behind water distribution systemdynamics. Municipal water demands are commonly clas-sified according to the nature of the user. The generalclassifications are customer consumption, nonrevenuewater, and fire flow demand. Customer consumption iscomputed on the basis of various customer types or cat-egories, which include single and multifamily residen-tial (domestic and irrigation), industrial (e.g., manufac-turing plants), commercial (e.g., restaurants, shoppingmalls, and office buildings), government (e.g., city andfederal buildings), recreational (e.g., parks and golfcourses), institutional (e.g., schools and universities),and agricultural (e.g., livestock). Nonrevenue water rep-resents the flow lost through leakage, pipe breaks,unmetered services, unauthorized use, hydrant flushingactivities, as well as losses from accounting and metererrors. It is normally computed as the difference betweenthe total volume of water produced (annual water pro-

duction) and the total amount of water billed (annualmetered consumption). In the network model, nonrevenuewater is normally distributed uniformly across the nodes,unless measurements for specific zones are available.Nonrevenue water is system-specific and can be signifi-cant in systems operating under high pressures as leak-age increases with pressure.

Fundamental questions related to network demand. Waterdemand levels vary considerably over time and amongusers. In general, water consumption is driven by popu-lation and economic activity as well as weather patterns.In order for a hydraulic simulation to properly reflectsystem performance, accurate demand estimates must bedeveloped and incorporated into the model, but deter-mining peak design demands is not as straightforwardas it is sometimes assumed to be. Estimating networkdemands is related to three fundamental questions.

• How much water will be used?• How will actual water demand be represented in a

network model?• How will water use change as a function of time?The first question is linked to future demand projec-

tions, which are usually the focus of master planning orrehabilitation studies. Future demand projections ulti-mately are used for the design of new distribution facili-ties, such as booster stations, storage tanks, and pipes.They are also essential to determining the effects on theexisting distribution system. Demand forecasting is nei-ther simple nor certain, because the projections must takeinto account the average per capita level of demand, theestimated and projected changes in population, the vari-ability of demand (particularly as it relates to peak use),and the physical attributes of the system (which willchange with time). Natural caution usually leads to over-estimation of demands, which then results in excessiveadditional costs (Babayan et al, 2005).

The second question is connected to demand allocation.The purpose of demand allocation is to load the hydraulicnetwork model with demands at the nodes, given theavailable information. Water use occurring along theentire length of each pipe is spatially redistributed to theassociated end nodes in the model. Demand allocationis often applied with the process of model skeletonization.Because demand allocation preserves the hydraulic per-formance and integrity of the larger original system, theresulting reduced network model produces the samesteady-state results as the larger original model; however,this process must be more carefully assessed for surgeanalysis. Model skeletonization eventually changes theamount and location of demands, which in turn can affectthe reflection and dissipation of transient pressure waves.The effect of water distribution model skeletonizationfor surge analysis has been described in other research(Jung et al, 2007b).

The final question is related to the temporal variationin demand. Temporal demand variations for municipal

Surge modeling is important to safeguard against breaches in distribution system integrity.



water systems generally follow quasi (stepwise) steady-state analysis for the simplified model and a transient analy-sis for a more accurate simulation. Demand patterns areused to represent the characteristics of diurnal curves forthe various user types, typically set up in increments of 15,30, or 60 min, depending on the data available. This for-mulation assumes that system pressures are adequate sothat nodal demands are independent of nodal pressures.Under transient conditions, however, the nodal pressuresmay not be sufficient for supplying the imposed demands.

EFFECT OF PRESSURE-SENSITIVE DEMAND ON SURGE ANALYSIS

Models of real-world systems tend to be simplifiedrepresentations of these systems. Which features of theactual system are incorporated into the model and whichfeatures are not depend in part on what the modeler con-siders important with respect to the issues under discus-sion, the problem at hand, or the questions being asked(Loucks, 1992). The time-varying demand model, despiteits complexity, is generally simplified and represented aseither a constant (pressure-insensitive) base demand witha diurnal curve or as a pressure-sensitive orifice. The diur-nal curve is seldom used for surge models, however, andthe rapid pressure fluctuation inherent in surge analysismay render the constant demand assumption less valid. Amore realistic representation of demand fluctuation isrequired to provide more accurate transient modelingresults, estimate worst-case scenarios, and more cost-effectively design adequate surge-control devices.

The constant demand can be replaced with the pres-sure-sensitive demand formulation using an “equivalentorifice” needed to pass the discrete constant demand at thesteady system pressure. Eq 1 can be used to represent

pressure-sensitive demand with the calculated emittercoefficient from the given initial constant demand Qi,and initial pressure pi, as

Cemit � Qi /p�i

(2)

To investigate the effects of a pressure-sensitive demandin transients, the orifice relations shown in Eqs 1 and 2can be used to relate the difference in demands to thedifference in pressures as

Q – Qi � Cemit p� – Cemit p�

i = Cemit p�

i ��p

p

i��

�

– 1� (3)

Because Cemitp�i = Qi, Eq 3 can be represented as

Q – Qi � Qi ��p

p

i��

�

– 1� (4)

The difference between the demands calculated inEq 4 is the type of error that arises in a hydraulic solu-tion when demand is assumed to be independent of thejunction pressure. More specifically, the assumption ofconstant demand causes an error whenever the junc-tion pressure is different from its initial value. For exam-ple, if a constant demand of 100 gpm is assigned withan initial pressure of 100 psi, the resulting demand dif-ference of the pressure-insensitive demand will vary asshown in Figure 2.

As Figure 2 illustrates, the demand difference is posi-tively increased as the junction pressure is increased, whichimplies that the junction node produces a greater demandas it experiences a positive surge in the transient. Becausethe increased demand from a positive surge causes moreenergy to dissipate, the corresponding junction pressure ofthe pressure-sensitive demand is lower than that of the

constant demand. Similarly, the junc-tion node produces less demand as itexperiences a negative surge in thetransient; therefore, the corre-sponding junction pressure of thepressure-sensitive demand is higherduring a negative surge than that ofthe constant demand. This charac-teristic of pressure-sensitive demandis important because models usingthe constant-demand assumptiontend to overestimate or underesti-mate the transient pressure condi-tions and lead to the overdesign ofsurge-protection devices, resultingin unnecessary additional costs.

Another important motivationfor conducting pressure-sensitivedemand for surge analysis is waterquality considerations. One of thechallenging problems in the man-agement of distribution system

-100

-80

-60

-40

-20

0

20

40

60

-100 -80 -60 -40 -20 0 20 40 60 80 100

Pressure Difference (H – Hi)—psi

Dem

and

Dif

fere

nce

(Q

– Q

i)—g

pm

FIGURE 2 Error of pressure-insensitive demand

H—head, Q—flow rate



water quality is that contaminants can intrude into pipesthrough leaks from reduced- or negative-pressure tran-sients. As shown in Eq 1, a negative- or low-pressuretransient (arising from a power failure or an intermittentor interrupted supply, for example) increases the risk ofbackflow and potential system contamination.

In summary, the assumption of constant demand insurge analysis ignores the pressure-sensitive characteris-tic inherent in actual pipeline sys-tems. Demand and pressure ateach junction node continuouslyvary, and the accurate represen-tation of this fluctuation is essen-tial in order to provide accuratetransient modeling results for suf-ficient system protection. To moreaccurately evaluate both systemperformance and the ultimatecost of strengthening the system,the constant demand model canbe replaced by a pressure-sensi-tive orifice model. The subsequentsection explores the use of thismodel in two case studies andcompares results with those forpressure-insensitive demand.

CASE STUDIESIn the following case studies,

surge analysis results of the pres-sure-sensitive demand modelwere compared with those ofpressure-insensitive (constant)demand formulations. In partic-ular, these studies highlighted thelimitations of pressure-insensi-tive demand for surge analysis.For all examples, the orificeswere placed at the elevation oftheir respective nodes. All of thetransient modeling results pre-sented here can be obtained usingthe method of characteristics(Wylie & Streeter, 1993) or thewave characteristic method (Bou-los et al, 2006; Wood et al,2005a) and can be reproducedusing available commercial or in-house water-hammer codes.

Case study 1: A small pipelinesystem. The first case study usedthe small water pipeline systemshown in Figure 3. This systemconsisted of a 100-m (328.1-ft)head reservoir feeding a networkof five pipe sections and five

junctions. The diameter, length, Hazen-Williams rough-ness coefficient, and wave speed for each pipe were 1 m(3.3 ft), 1,000 m (3,280.8 ft), 100, and 1,000 m/s(3,280.8 fps), respectively. The elevation of each junctionwas assumed to be 0 m. Each junction node had an exter-nal demand of 0.2 m3/s (7.06 cfs) so the total dischargefrom the upstream reservoir was 1 m3/s (35.3 cfs). Arapid demand decrease over a 1-s time period at the ter-

70

80

90

100

110

120

130

Time—s

Pre

ssu

re—

m

0 10 20 30 40 50

Junction 1 Junction 3 Junction 5

FIGURE 4 Pressure head profiles using pressure-insensitive demand

70

80

90

100

110

120

130

0 10 20 30 40 50

Time—s

Pre

ssu

re—

m

FIGURE 5 Pressure head profiles using pressure-sensitive demand

Junction 1 Junction 3 Junction 5

Elevation = 100 m (328.1 ft)

0.2 m3/s(7.06 cfs)

0.2 m3/s(7.06 cfs)

0.2 m3/s(7.06 cfs)

0.2 m3/s(7.06 cfs)

0.2 m3/s(7.06 cfs)

1 2 3 4 5

FIGURE 3 A small pipeline system

Junction



minal junction 5 was initiated at 5 s to introduce a tran-sient condition.

Figures 4 and 5 show the transient head profiles atjunctions 1, 3, and 5 using pressure-insensitive and pres-sure-sensitive demands, respectively. As shown in thefigures, the initial steady pressures at junctions 1, 3, and5 were identical because the emitter coefficient of Eq

1was calculated from the initial steady head and flow,and the head profiles of both Figures 4 and 5 were steadyfor the first 5 s. In addition, the initial positive surges inboth figures for junction 5 were identical at 121.15 m(397.49 ft). After creating the initial surge, the surgewave of the pressure-insensitive demand was propa-gated without any disturbance except that the frictionloss along the pipeline caused a slight dissipation (Fig-ure 4). In contrast, the surge wave of the pressure-sen-sitive demand experienced dramatic pressure dissipa-tion when it passed the junctions (Figure 5). Therationale for this difference is that the positive surgepressure caused a greater discharge (higher than theconstant demand) through the demand junction, andthen the demand increase caused a negative surge thatwas propagated in both upstream and downstreamdirections. Therefore, the negative surge created fromthe pressure-sensitive demand interacted with the initialpositive surge, causing some pressure dissipation. Whenthe initial positive surge reached the upstream reser-voir, the behavior of pressure-sensitive demand was the

opposite of the initial positive surge because the posi-tive surge was converted into a negative surge. The neg-ative surge caused a lower discharge (lower than theconstant demand) through the demand junction, andthen the resulting demand decrease caused a positivesurge, which dissipated the reflected negative surgefrom the reservoir.

Table 1 shows the maximum positivesurge (obtained by subtracting the maximumtransient pressure from the initial steadypressure), the maximum negative surge(obtained by subtracting the minimum tran-sient pressure from the initial steady pres-sure), and their differences for all five junc-tions and for both pressure-insensitivedemand and pressure-sensitive demandanalyses. Because the pressure-insensitivedemand model cannot accurately represent

the pressure-sensitive characteristics of a nodal demand,the difference between the two transient demand mod-els increased as the distance from the location causing thetransient (junction 5) increased. For example, the dif-ference in the maximum pressure at junction 5 was neg-ligible (1.9/26.1 = 7%) whereas the maximum pressuredifference for junction 1 was significant (5.7/20 = 29%).In addition, the reflected surge wave shown in Table 1provided the worst results, with more than 100% dif-ference for all junctions. Certainly, in this particularcase with the pressure-insensitive demand, estimatingthe occurrence of local vacuum conditions and cavitationat specific locations or contaminant intrusion duringnegative transients would be exaggerated. The differ-ences shown in Table 1 were within the first cycle of asurge wave normally used to estimate the maximum andminimum pressures in the system. Therefore, the cor-responding surge-protection device, especially under thenegative transient, could well be overdesigned.

Furthermore, the maximum positive surge of pres-sure-insensitive demand at junction 5 of 28.0 m (91.9 ft)

Maximum Positive Surge—m (ft) Maximum Negative Surge—m (ft)

Pressure- Pressure- Pressure- Pressure-insensitive sensitive insensitive sensitive

Junction Demand Demand Difference Demand Demand Difference

1 25.7 (84.2) 20.0 (65.5) 5.7 (18.7) –22.6 (–74.2) –9.8 (–32.1) 12.8 (42.1)

2 26.4 (86.5) 21.4 (70.3) 4.9 (16.2) –22.0 (–72.2) –9.6 (–31.4) 12.4 (40.8)

3 27.0 (88.6) 23.0 (75.3) 4.1 (13.3) –21.8 (–71.4) –9.7 (–31.9) 12.0 (39.5)

4 27.6 (90.4) 24.5 (80.4) 3.0 (10.0) –21.9 (–71.8) –10.2 (–33.6) 11.7 (38.3)

5 28.0 (91.9) 26.1 (85.5) 1.9 (6.4) –22.3 (–73.2) –11.1 (–36.4) 11.2 (36.8)

TABLE 1 Maximum positive and negative surges

The pressure-insensitive constant demand model canbe easily replaced with a pressure-sensitive orifice model.



was higher than the potential surge of 26.0 m (85.3 ft),which is defined as aV/g in which a is the wave speed of1,000 m/s (3,280 fps), V is the velocity of water in thepipeline at 0.255 m/s (0.837 fps), and g is the accelera-tion of gravity at 9.81 m/s2 (32.2 ft/s2). This increasedpressure that was greater than the potential surge afterthe initial flow stoppage is termed line packing andrefers to the increase in the storage capacity of a pipeline.Line packing occurs because only part of the flow isstopped by the first compression wave, and then theflow is stopped completely at the valve; thus, the pres-sure continues to rise, the pipe wall expands, and the liq-uid continues to be compressed. Packing varies with linediameter, wall thickness, and length. The potential surgeaV/g is inaccurate in certain cases and thus is likely tolead to poor design. The inadequacies of this simplisticmodeling approach for surge analysis have beendescribed in detail (Jung et al, 2007a). Of interest is thefact that the maximum positive surge of the pressure-sen-sitive demand model at junction 5 (26.1 m [85.5 ft])was almost the same as the potential surge. Becausepressure-sensitive demands at the upstream of junction5 caused negative surges, the negative surges were prop-agated to junction 5 after the head at junction 5 reachedthe potential surge (Figure 5).

Another major pitfall of pressure-insensitive demandis its incorrect independency on nodal elevation. Flowdischarge through an emitter is dependent on both ele-vation and pressure. Tables 2 and 3 list the maximumpositive surge, the maximum negative surge, and theirdifferences for the system shown in Figure 3 but with dif-ferent junction elevations of 20 m and –20 m, respec-tively. Because the system was pressurized and thedemand fixed, the maximum positive and negative surgesof the pressure-insensitive demand model for both ele-vations were identical to those shown in Table 1. Aslong as the total head is greater than the cavitation pres-sure, the surge wave of the pressure-insensitive demandmodel is independent of demand elevation. However,actual transient discharge through an emitter is depen-dent on the elevation. The higher elevation had the lowerstatic pressure, causing the larger emitter coefficient inEq 2 to maintain the same initial steady discharge. Theincreased emitter coefficient attributable to the higher ele-vation produced a greater discharge for a positive surgeand a lower discharge for a negative surge. The increaseddischarge caused a negative surge that interacted with theinitial positive surge, whereas the decreased dischargehad the opposite effect. Therefore, higher elevation ledto increased surge pressure dissipation. Figure 6 shows




1 25.7 (84.2) 20.8 (68.2) 4.9 (16.0) –22.6 (–74.2) –11.3 (–37.0) 11.3 (37.1)

2 26.4 (86.5) 22.1 (72.5) 4.3 (14.0) –22.0 (–72.2) –11.0 (–36.2) 11.0 (36.1)

3 27.0 (88.6) 23.4 (76.9) 3.6 (11.7) –21.8 (–71.4) –11.1 (–36.5) 10.7 (34.9)

4 27.6 (90.4) 24.8 (81.3) 2.8 (9.2) –21.9 (–71.8) –11.6 (–38.0) 10.3 (33.8)

5 28.0 (91.9) 26.1 (85.5) 1.9 (6.4) –22.3 (–73.2) –12.4 (–40.7) 9.9 (32.5)

TABLE 3 Maximum positive and negative surges with decreased elevation (–20 m)




1 25.7 (84.2) 18.8 (61.7) 6.9 (22.5) –22.6 (–74.2) –7.9 (–25.9) 14.7 (48.3)

2 26.4 (86.5) 20.5 (67.2) 5.9 (19.3) –22.0 (–72.2) –7.7 (–25.3) 14.3 (46.9)

3 27.0 (88.6) 22.3 (73.1) 4.7 (15.5) –21.8 (–71.4) –7.9 (–25.9) 13.9 (45.6)

4 27.6 (90.4) 24.2 (79.3) 3.4 (11.2) –21.9 (–71.8) –8.4 (–27.6) 13.5 (44.2)

5 28.0 (91.9) 26.1 (85.5) 1.9 (6.4) –22.3 (–73.2) –9.3 (–30.5) 13.0 (42.7)

TABLE 2 Maximum positive and negative surges with increased elevation (20 m)



the surge pressure at junction 1for pressure-insensitive demandand pressure-sensitive demandwith three elevations (0, 20, and–20 m). As shown in the figure,the highest elevation case (20 m)of the pressure-sensitive demandcaused the greatest surge pressuredissipation.

Case study 2: A pipe network sys-tem. To highlight the drawbacksof the pressure-insensitive demandmodel for surge analysis on alarger, more complex system, thepressure-insensitive and pressure-sensitive demand models wereapplied to an actual water distri-bution network (Figure 7). Thesystem comprised 1,639 junctions,2,088 pipes, 23 wells, 23 pumps,and 1 storage tank. (The identityof the corresponding water util-ity has been withheld because ofsecurity concerns.) For this exam-ple, the transient was initiatedfrom pump trips at 5 s.

Figure 8 shows the transienthead profiles at junction 242 usingpressure-insensitive and pressure-sensitive demand analysis. Asshown in the figure, both modelsproduced the same steady hy-draulic equilibrium condition (69.6m [228.4 ft]), but the transientresponse for the pressure-sensitivedemand model differed from thatof the pressure-insensitive demandmodel. The maximum and mini-mum pressures of junction 242 forthe pressure-insensitive demandmodel were 117.9 m (386.8 ft) and–10.1 m (–33.1 ft), whereas thoseof the pressure-sensitive demandmodel were significantly lower at66.8 m (219.2 ft) and 4.6 m (15.1ft). Figure 9 shows the difference inthe maximum and minimum pres-sures for the two demand models.The greatest difference in the max-imum pressures (233.9 m [767.5ft] for pressure-insensitive demandand 61.9 m [203.2 ft] for pressure-sensitive demand) was 172.0 m(564.3 ft) at junction 30, indicatingthat the maximum pressure of thepressure-insensitive demand model

–30.0

–20.0

–10.0

0.0

10.0

20.0

30.0

0 10 20 30 40 50

Time—s

Su

rge

Pre

ssu

re—

m

Pressure-insensitive demand Pressure-sensitive demand at –20-m elevation Pressure-sensitive demand at 0-m elevation Pressure-sensitive demand at 20-m elevation

FIGURE 6 Surge pressure profiles at junction 1 at different elevations

Pump tripMeasurement location junction 242

FIGURE 7 A network system

-20

20

60

100

140

Time—s

Pre

ssu

re—

m

Pressure-insensitive demandPressure-sensitive demand

0 20 40 60 80 100

FIGURE 8 Pump trip transient results at junction 242



was 278% higher than that of thepressure-sensitive demand model.Similarly, the maximum differencein the minimum pressures (–10.1m [–33.2 ft] for pressure-insensi-tive demand and 42.8 m [140.5 ft]for pressure-sensitive demand) was53.0 m (173.7 ft) at junction 30,indicating that the minimum pres-sure of the pressure-insensitivedemand model was 124% lowerthan that of the pressure-sensitivedemand model. These resultsclearly demonstrated that the pres-sure-insensitive demand modelwas unable to estimate the water-hammer phenomena correctly andoften exaggerated surge waves inthe distribution system. As a re-sult, use of the pressure-insensi-tive demand model may lead tooverdesign of surge-suppressionand -protection devices. However,this overdesign does not necessar-ily convey a higher degree of safetyunless all hydraulic transient con-ditions have been properly ana-lyzed. An overdesigned systemsometimes can be more detrimen-tal than an underdesigned onebecause the overdesigned hy-draulic devices themselves maydeteriorate the system’s surgeresponse (Jung & Karney, 2006;Karney & McInnis, 1990).

Another advantage of the pres-sure-sensitive demand model is itsability to more accurately estimatecontaminant intrusion in waterdistribution systems. Contami-nants can intrude into pipesthrough leaks during a negative-pressure transient; the surge modelusing pressure-sensitive demandcan simulate the location, amount,and duration of these intrusions.The case study of Figure 7 wasapplied again with the assumptionthat 10% of water demand at alljunctions was discharged (lost) asleakage. The emitter coefficientaccounting for the leakage at thedemand junction was calculatedusing Eq 2 on the basis of 10% ofthe demand. This emitter coeffi-cient was applied for the intrusion

0

50

100

150

200

2 300 602 892 1186 1486 1788 2096 2396 2696 3056 3354

Junction Identification

Pre

ssu

re D

iffe

ren

ce—

m

Maximum pressureMinimum pressure

FIGURE 9 Pressure difference between pressure-insensitive and pressure-sensitive demands

Junction numbers are for identification purposes only and do not follow any specific order.

Locations of negative pressure (intrusion)

FIGURE 10 The locations of intrusion using the pressure-sensitive demand model

Locations of negative pressure (intrusion)

FIGURE 11 The locations of intrusion using the pressure-insensitive demand model



calculation during negative transients. Figure 10 showsthe locations of negative pressure (intrusion) using thepressure-sensitive demand model. For the given tran-sient condition, 23 nodes experienced contaminant intru-sion, and the corresponding intruded volume was 0.064L (0.017 gal). Similarly, the pressure-insensitive demandmodel was used to estimate the areas of possible cont-aminant intrusion for the system under identical tran-sient conditions. Figure 11 shows that the pressure-insensitive demand model resulted in 379 nodesexperiencing the negative transient pressures. Theseresults demonstrated that the pressure-insensitivedemand model may significantly overestimate the riskof contaminant intrusion and lead to an increased costfor surge-protection devices. However, even though thepressure-sensitive demand model may reduce the com-puted occurrence of intrusion in a system, the actualoccurrence and amount of intrusion are also a func-tion of other important factors, such as surroundingsoil condition and standing water.

CONCLUSIONManaging and protecting water supply and distribu-

tion systems from contamination threats and emergencysituations require implementation of best operationalpractices (e.g., maintaining a positive water pressure andan adequate level of disinfectant residual throughout thedistribution system), more rigorous applications of exist-ing engineering standards, and the use of surge modelingto predict and eliminate potential weak spots.

Surge modeling is important to safeguard againstbreaches in distribution systems’ integrity. The assump-tion of pressure-insensitive demand (i.e., demand-dri-ven analysis) has been widely applied to surge analysis,but this modeling approach may be problematic for sev-eral reasons.

• First, it ignores the implicit relationship betweendemand and pressure inherent in actual pipeline sys-tems. Accurate transient modeling requires the accuraterepresentation of fluctuating demands. A positive-pres-sure surge causes a higher discharge through the junc-tions, which dissipates the initial positive surge. Simi-larly, a negative-pressure surge yields a lower dischargethrough the junctions, causing a positive surge thatdissipates the initial negative surge. Case studies showedthat the surge wave of pressure-sensitive demand expe-rienced dramatic pressure dissipation when it passed thedemand junctions whereas the surge wave of pressure-insensitive demand was propagated without any dis-turbance except from the friction loss along thepipeline.

• Second, the transient results of the two demandmodels were quite different even within the first cycle ofa surge wave normally used to estimate the maximumand minimum system pressures. The pressure-insensitivedemand model tended to exaggerate a surge result, which

could lead to overdesign of surge-protection devices.However, this overdesign does not readily imply a higherdegree of safety unless all hydraulic transient conditionshave been properly analyzed.

• Third, because of its fixed demand characteristic,pressure-insensitive demand is insensitive to nodal ele-vation as long as the total head is above the cavitationpressure. However, actual transient discharge through anemitter is dependent on the elevation. The higher eleva-tion causes more surge dissipation because the low staticpressure produces more demand from the positive surgeand less demand for the negative surge.

• Finally, the pressure-sensitive demand model canmore accurately assess the effect of transient-inducedcontaminant intrusions. The case study described in thisarticle demonstrated that the pressure-insensitive demandmodel exaggerated a surge wave on the distribution sys-tem and significantly overestimated the risk of contam-inant intrusion. The pressure-sensitive demand modelalso offers the capability of being extended to simulatethe amount of intrusion from the given or assumed leak-age amount.

Every hydraulic modeling exercise requires that certainassumptions and approximations be made to simplifythe problem and make it possible or easy to obtain asolution. However, the assumptions made while solvingthe problem should be reasonable and justifiable. Becausewater use or demand continuously varies rapidly withtime and with local pressure (which strongly influencesthe surge response in the distribution system), the assump-tion of pressure-insensitive demand is not valid for surgeanalysis, and the results based on the assumption may begrossly incorrect. The pressure-insensitive constantdemand model can be easily replaced with a pressure-sen-sitive orifice model. This approach is justified by itsintrinsically more accurate estimation of water-hammerphenomena as well as its proper assessment and morecost-effective selection of surge-protection and -controlstrategies. As this research demonstrated, a pressure-sen-sitive demand model can provide more accurate infor-mation than that of a constant demand model for surgeanalysis. Independent field testing should be carried outto further validate this finding.

ABOUT THE AUTHORSBong Seog Jung is a professional engineer with MWH Soft in Arcadia,Calif. He has BS and MS degrees inenvironmental engineering fromPusan National University in Pusan,South Korea, and a PhD in civil engineering from the University ofToronto in Ontario. For the past eight

years, his research and consulting experience hasfocused on hydraulic transients and optimization ofwater distribution systems. Paul F. Boulos (to whom



REFERENCESAng, W.K. & Jowitt, P.W., 2006. Solution for Water Distribution Sys-

tems Under Pressure-Deficient Conditions. Jour. WaterResource Planning & Mgmt., 132:3:175.

Babayan, A.; Kapelan, Z.; Savic, D.; & Walters, G., 2005. Least-CostDesign of Water Distribution Networks Under Demand Uncer-tainty. Jour. Water Resource Planning & Mgmt.—ASCE,131:5:375.

Boulos, P.F.; Lansey, K.E.; & Karney, B.W., 2006. ComprehensiveWater Distribution Systems Analysis Handbook for Engi-neers and Planners (2nd ed.). MWH Soft Inc. Publ.,Broomfield, Colo.

Boulos, P.F.; Karney, B.W.; Wood, D.J.; & Lingireddy, S., 2005.Hydraulic Transient Guidelines for Protecting Water Distribu-tion Systems. Jour. AWWA, 97:5:111.

Chaudhry, M.H., 1987. Applied Hydraulic Transients (2nd ed.). VanNostrand Reinhold, New York.

Funk, J.E.; VanVuuren, S.J.; Wood, D.J.; LeChevallier, M.W.; &Friedman, M., 1999. Pathogen Intrusion Into Water DistributionSystems Due to Transients. Proc. ASME/JSME Joint FluidsEngrg. Conf., San Francisco.

Ghidaoui, M.S.; Zhao, M.; McInnis, D.A.; & Axworthy, D.H., 2005. AReview of Water-hammer Theory and Practice. Appl. Mech.Rev., 58:49.

Gullick, R.W.; LeChevallier, M.W.; Svindland, R.C.; & Friedman, M.J.,2004. Occurrence of Transient Low and Negative Pressures inDistribution Systems. Jour. AWWA, 96:11:52.

Gupta, R. & Bhave, P.R., 1996. Comparison of Methods for Predict-ing Deficient Network Performance. Jour. Water ResourcePlanning & Mgmt.—ASCE, 122:3:214.

Jowitt, P.W. & Xu, C., 1993. Predicting Pipe Failure Effects in WaterDistribution Networks. Jour. Water Resource Planning &Mgmt.—ASCE, 119:1:18.

Jung, B.S.; Karney, B.W.; Boulos, P.F.; & Wood, D.J., 2007a. TheNeed for Comprehensive Transient Analysis of DistributionSystems. Jour. AWWA, 99:1:112.

Jung, B.S.; Boulos, P.F.; & Wood, D.J., 2007b. Pitfalls of Water Distri-bution Model Skeletonization for Surge Analysis. Jour.AWWA, 99:12:87.

Jung, B.S. & Karney, B.W., 2006. Hydraulic Optimization of Tran-sient Protection Devices Using GA and PSO Approaches.Jour. Water Resource Planning & Mgmt.—ASCE, 132:1:44.

Jung, B.S. & Karney, B.W., 2004. Fluid Transients and Pipeline Opti-mization Using GA and PSO: The Diameter Connection. UrbanWater Jour., 1:2:167.

Karim, M.R.; Abbaszadegan, M.; & LeChevallier, M.W., 2003. Poten-tial for Pathogen Intrusion During Pressure Transient. Jour.AWWA, 95:5:134.

Karney, B.W. & Fillion, J.R., 2003. Energy Dissipation Mechanismsin Water Distribution Systems. Proc. Pumps, Electromechani-cal Devices, and Systems (PEDS) Conf., Valencia, Spain.

Karney, B.W. & McInnis, D., 1990. Transient Analysis of Water Dis-tribution Systems. Jour. AWWA, 82:7:62.

Kirmeyer, G.J.; Friedman, M.; Martel, K.; Howie, D.; LeChevallier,M.W.; Abbaszadegan, M.; Karim, M.; Funk, J.; & Harbour, J.,2001. Pathogen Intrusion Into the Distribution System.AwwaRF, Denver.

Lansey, K.E. & Boulos, P.F., 2005. Comprehensive Handbook onWater Quality Analysis in Distribution Systems. MWH Soft Inc.Publ., Broomfield, Colo.

LeChevallier, M.W., 1999. The Case for Maintaining a DisinfectantResidual. Jour. AWWA, 91:1:86.

LeChevallier, M.W.; Gullick, R.W.; Karim, M.R.; Friedman, M; & Funk,J.E., 2003. Potential for Health Risks From Intrusion of Contam-inants Into the Distribution System From Pressure Transients.Jour. Water & Health, 1:1:3.

LeChevallier, M.W.; Gullick, R.; & Karim, M., 2002. The Potential forHealth Risks From Intrusion of Contaminants Into the Distribu-tion System From Pressure Transients. EPA Distribution Sys-tem White Paper, Washington.

Loucks, D.P., 1992. Water Resource Systems Models: Their Role inPlanning. Jour. Water Resource Planning & Mgmt.—ASCE,118:3:214.

McInnis, D.A., 2004. A Relative Risk Assessment Framework forEvaluating Pathogen Intrusion During Transient Events inWater Pipelines. Urban Water Jour., 1:2:113.

McInnis, D.A. & Karney, B.W., 1995. Transients in Distribution Net-works: Field Tests and Demand Models. Jour. Hydraul. Engrg.,121:3:218.

Ndambuki, J.M., 2006. Water Quality Variation Within a DistributionSystem: A Case Study of Eldoret Municipality, Kenya. Proc.Environmentally Sound Technology in Water Resources Man-agement Conf., Gaborone, Botswana.

NRC (National Research Council), 2006. Drinking Water DistributionSystems: Assessing and Reducing Risks. National AcademiesPress, Washington.

Thorley, A.R.D., 1991. Fluid Transients in Pipeline Systems. D&LGeorge Ltd., Herts, England.

Wood, D.J.; Lingireddy, S.; & Boulos, P.F., 2005a. Pressure WaveAnalysis of Transient Flow in Pipe Distribution Systems. MWHSoft Inc. Publ., Broomfield, Colo.

Wood, D.J.; Lingireddy, S.; Boulos, P.F.; Karney, B.W.; & McPherson,D.L., 2005b. Numerical Methods for Modeling Transient Flowin Distribution Systems. Jour. AWWA, 97:7:104.

Wylie, E.B. & Streeter, V.L., 1993. Fluid Transients in Systems. Pren-tice-Hall, Englewood Cliffs, N.J.

correspondence should be addressed) is the presidentand chief operating officer of MWH Soft, 380 Inter-locken Crescent, Ste. 200, Broomfield, CO 80021; [email protected]. Don J. Wood is professoremeritus in the Department of Civil Engineering atthe University of Kentucky in Lexington.

Date of submission: 04/06/07Date of acceptance: 08/24/07

If you have a comment about this article,please contact us at [email protected].


effect of pressure-sensitive demand on surge analysis m · pdf fileeffect of...

Documents