Pitfalls of water distribution model skeletonization for surge analysis.

2007 © American Water Works Association

JUNG ET AL | 99 :12 • JOURNAL AWWA | PEER-REVIEWED | DECEMBER 2007 87

Pitfalls of water distributionmodel skeletonization for surge analysis

Skeletonization is the process of representing a water distribution system model by only

selected pipes. Skeletonized models normally are adequate for master planning and energy

studies, but the degree of skeletonization that is acceptable for surge analysis is an often-raised

question. Most of the guidelines used for skeletonizing hydraulic network models do not

apply for surge modeling. Replacing two or more pipes in parallel or series into an equivalent

pipe with the same carrying capacity and trimming dead-end mains can be readily applied for

steady-state analysis with virtually no effect on the resulting flows and pressures, but their

effect on the system transient response can be significant. Moreover, the ratio of the pipe

diameters greatly affects the transient pressure wave attenuation. In addition, dead ends, which

may be caused by closure of check valves, lock pressure waves into the system in a cumulative

fashion, and wave reflections will double both positive and negative pressures. The rules of

skeletonization ignore the transient interaction of transient pressure waves in the different

components and pipe properties of a water distribution system. In this article, case studies

highlight the pitfalls of skeletonization in pressure surge analysis and support the conclusion

that surge analysis requires a detailed model to accurately estimate transient pressure

extremes in a water distribution system. A highly skeletonized model may overlook critical

locations that are vulnerable for intrusion of potentially contaminated water.

BY BONG SEOG JUNG,

PAUL F. BOULOS,

AND DON J. WOOD

apid changes in pressure and flow conditions (e.g., rapid valve closures orpump stoppages, hydrant flushing), whether caused by design or acci-dent, can create pressure surges of excessive magnitude. These transientpressures are superimposed on the normal static pressures present in thewater line at the time the transient occurs and can degrade the integrity

of the water distribution system. The total force acting within a pipe is obtainedby summing the steady-state and transient pressures in the line. Therefore, theseverity of transient pressures must be accurately determined so that the watermains can be properly designed to withstand these additional loads. In fact, pipesare often characterized by their pressure ratings, which define the pipes’ mechan-ical strength and significantly influence their cost.

BACKGROUNDTransients. Transients have been responsible for equipment failure, pipe rupture,

separation at bends, and the backflow of dirty water into the distribution systemvia intrusion. High-flow velocities can remove protective scale and tubercles andincrease the contact of the pipe with oxygen, all of which will increase the rate ofcorrosion. Uncontrolled pump shutdown can lead to the undesirable occurrence ofwater column separation, which can result in catastrophic pipeline failures assevere pressure rises following the collapse of the vapor cavities. Vacuum condi-

R

88 DECEMBER 2007 | JOURNAL AWWA • 99 :12 | PEER-REVIEWED | JUNG ET AL


tions can create high stresses and strains that are muchgreater than those occurring during normal operatingregimes. Vacuums can cause the collapse of thin-walledpipes or reinforced concrete sections, particularly if thesesections were not designed (i.e., pipes with a low pressurerating) to withstand such strains.

Cavitation occurs when the local pressure is loweredto the value of vapor pressure at the ambient temperature.

At this pressure, gas within the water is gradually releasedand the water starts to vaporize. When the pressure recov-ers, water enters the cavity caused by the gases and collideswith whatever confines the cavity (i.e., another mass ofwater or a fixed boundary), resulting in a pressure surge.In this case, both vacuum and strong pressure surges arepresent, a combination that may result in substantial dam-age. The main issue here is that accurate estimates are dif-ficult to achieve, particularly because the parametersdescribing the process are not yet determined during design.Moreover, the vapor cavity collapse cannot be effectivelycontrolled. In less drastic cases, strong pressure surges maycause cracks in internal lining, damage connections betweenpipe sections, and destroy or cause deformation to equip-ment such as pipeline valves, air valves, or other surge-protection devices. Sometimes the damage is not realizedat the time but results in intensified corrosion that, com-bined with repeated transients, may cause the pipeline tocollapse in the future (Boulos et al, 2006; Boulos, 2005).

Health and water quality implications. Transient condi-tions can have significant water quality and health impli-cations (Boulos, 2005; Boulos et al, 2005). Transients cangenerate high intensities of fluid shear and may causeresuspension of settled particles as well as biofilm detach-ment. Moreover, low-pressure transients may promotethe collapse of water mains; leakage into the pipes at loosejoints, cracks, and seals under subatmospheric conditions;

and backsiphonage andpotential intrusion ofuntreated, possibly conta-minated groundwater in thedistribution system.Pathogens or chemicalsclose to the pipe canbecome a potential conta-mination source. Studieshave confirmed that soiland water samples collectedimmediately adjacent to

water mains can contain high fecal coliform concentrationsand viruses (Karim et al, 2003; Kirmeyer et al, 2001).

Other researchers reported the existence of low- andnegative-pressure transients in several distribution sys-tems (LeChevallier et al, 2003). In a study of intrusionoccurrences in actual distribution systems, 15 surges wereobserved that resulted in a negative pressure (Gullick etal, 2004). Recent research confirmed that negative-pres-sure transients can occur in the distribution system andthat the intruded water can travel downstream from thesite of entry (Friedman et al, 2004). Locations with thehighest potential for intrusion were sites experiencingleaks and breaks, areas of high water table, and floodedair-vacuum valve vaults.

In the event of a large intrusion of pathogens, the chlo-rine residual normally sustained in drinking water dis-tribution systems may be insufficient to disinfect conta-minated water. Indeed, intrusion of as little as 0.05%sewage contamination can cause substantial chlorine

decay and would require a cor-respondingly substantial increasein time in order to inactivatepathogens (Baribeau et al, 2005).For this reason, water utilitiesshould never overlook the effectof pressure surges in their distri-bution systems. Any optimizeddesign that fails to properlyaccount for pressure-surge effectsis likely to be, at best, subopti-mal and, at worst, completelyinadequate.

Low water pressure in distri-bution systems is a well-knownrisk factor for outbreaks ofwaterborne disease (Hunter,

Transients have been responsible for equipmentfailure, pipe rupture, separation at bends, and thebackflow of dirty water into the distribution systemvia intrusion.

Reservoir P5

P4 P3J3

J4

P1

P2

J2 J1

1 m3/s demand

FIGURE 1 Case 1: A small water pipeline system

J—junction, P—pipe


1997). In 1997, a massive epi-demic of multidrug-resistanttyphoid fever was reported inthe city of Dushanbe, Tajik-istan; affecting about 1% of thecity’s population, the outbreakcaused 8,901 cases of typhoidfever and 95 deaths. Low waterpressure and frequent wateroutages had contributed to thewidespread increase in conta-mination within the distribu-tion system (Hermin et al,1999). More recently, a Giardiaoutbreak was reported at aNew York trailer park in April2002, causing six residents tobecome seriously ill (Blackburnet al, 2004). Contaminationwas attributed to a power out-age, which created a negative-pressure transient in the distri-bution system. This allowedcontaminated water to enterthe system through either a cross-connection inside amobile home or a leaking underground pipe that wasnear sewer crossings. During the same period (February2001 to May 2002), a large-scale control study of therisk factors for sporadic cryptosporidiosis found a strongassociation between self-reported diarrhea and reportedlow water pressure (Hunter et al, 2005).

Causes of pressure surge. Transient conditions thatcan allow intrusion to occur are caused by suddenchanges in water velocity attributable to loss of power,sudden valve or hydrant closure or opening, a mainbreak, fire flow, or an uncontrolled change in on/off

pump status (Boyd et al, 2004). Although not all intru-sions are caused by pressure transients, transient-inducedintrusions can be minimized by knowing the causes ofpressure surges, defining the system’s response to surges,and estimating the system’s susceptibility to contamina-tion when surges occur (Friedman et al, 2004). Pressuretransients in water distribution systems are usually mostsevere at pump stations and control valves, in high-ele-vation areas, in locations with low static pressures, and

in remote locations that are at a distance from overheadstorage (Friedman et al, 2004).

Additionally, the water distribution system must some-times deliver large fire demands at adequate pressure.Although these fire demands occur infrequently, they maybe a highly constraining factor in pipeline design. There-fore, design procedures should evaluate the ability of thesystem to meet fire-fighting demands at all relevanthydrant locations. Even though the occurrence of simul-taneous fires at all possible locations is not realistic, anarray of fire-fighting demand patterns must still be con-sidered. Under transient conditions, it is important to

anticipate both the estab-lishment of fire flows andtheir ultimate curtailment, aprocess that often unfoldsrapidly in time and can cre-ate significant transient pres-sures, particularly if firecrews receive little trainingor instruction (Jung & Kar-ney, 2004b). Accurate mod-eling is essential in this case

because neglecting some influences could lead to wrongconclusions and poor decisions.

Controlling transients. Several devices can be used tocontrol transients in pipeline systems (Boulos et al, 2006;2005; Wood et al, 2005a). Devices to control pressuresurge operate on the general principles of storing water orotherwise delaying the change of flow or dischargingwater from the line so that rapid or extreme fluctuationsin the flow regime are minimized. Devices such as pres-


Transient conditions can have significant waterquality and health implications.

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FIGURE 2 Pressure head profile at junction J1 with three levels of skeletonization


sure-relief valves, surge-anticipation valves, surge vessels,surge tanks, pump-bypass lines, or any combinationthereof are commonly used to control maximum pres-sures. Minimum pressures can be controlled by increas-ing pump inertia or by adding surge vessels, surge tanks,air-release/ vacuum valves, pump-bypass lines, or anycombination of these components. The overriding ob-jective is to reduce the rate at which flow changes occur.

Recent studies have included a detailed transient flowchart that provides a comprehensive guide selecting com-ponents for surge control and suppression in water dis-tribution systems (Boulos et al, 2006; 2005). These devicesoffer the only practical opportunity to protect the publicfrom potential intrusion of contaminants caused by lowor negative pressure. Other researchers used optimiza-tion theory to determine the optimal placement and siz-ing of open surge tanks and pressure-relief valves to con-trol hydraulic transients in a pipeline system (Jung &Karney, 2006). A comprehensive surge analysis shouldbe performed on a representative network model of thedistribution system to properly locate and size the most

effective combination of surge-protection devices.

Computer modeling. Althoughlooped networks are generallyless susceptible to objectionablepressure transients than are sin-gle, long transmission main sys-tems, they must still be protectedagainst low- or negative-pressuretransients. Computer-basedmathematical models offer themost effective and viable meansof analyzing hydraulic transientsin water distribution systems.These models provide a powerfultool for determining the extentof pressure wave attenuationswithin the water distribution sys-tem environment and calculatingtheir effect on the resulting flowsand pressures. The models canbe used to develop and evaluatedesign and operational alterna-tives that address the needs anddeficiencies identified in thehydraulic transient analysis andto prepare contingency plans. Ina recent study identifying severalof the misconceptions or limita-tions of simplified rules for surgeanalysis, the authors concludedthat only systematic andinformed surge analysis can beexpected to resolve complex tran-sient characterizations and ade-

quately protect distribution systems from the vagariesand challenges of rapid transients (Jung et al, 2007).

Skeletonization techniques are widely used to simplifythe reduction of large water distribution network modelsto a manageable size for analysis. They make use of data-base management and hydraulic equivalency theory toreduce excessive pipe segmentation while maintainingthe hydraulic behavior of the larger original model. Appli-cations include merging series pipes and/or consolidat-ing parallel pipes into a single hydraulically equivalentpipe with the same carrying capacity, removing pipes lessthan a specified diameter, trimming dead-end mains, andeliminating hydrant leads.

However, the application of skeletonization for surgeanalysis is questionable. Hydraulic equivalency theory ispredicated on steady-state equilibrium and ignores theinteraction of transient pressure waves in the differentpipe properties of a distribution system. The ratio of thepipe diameters has a significant effect on the transientpressure wave attenuation. Smaller-diameter pipes con-nected to larger mains amplify the surge waves and


J4

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Series Skeletonization

Dead-end Skeletonization

FIGURE 3 Maximum and minimum heads and their corresponding locations

J—junction (location)

Degree of Skeletonization

Reservoir

J3

J—junction

20 m

1,000 m 1,000 mJ2 J1

1 m3/s

FIGURE 4 Case 2: A sample system with a dead end


become more susceptible to the presence of water col-umn separation and subsequent collapse. The collapseof vapor cavity can result from flow reversal because ofhigher hydraulic head from a nearby storage tank. It cancreate extremely high-pressure spikes that can damagethe pipeline and the seals, leaving the system even morevulnerable to low-pressure conditions. At any disconti-nuity of pipe, wave reflections and transmissions occur,which often magnify or attenuate the transient pressurewave. The wave speed is also a function of the pipe mate-rial, diameter, and thickness.

Limited published work has addressed the relation-ship between the degree of model skeletonization and theaccuracy of the surge modeling results. Martin (2000)warned that oversimplified models may introduce error.Davis (2001) confirmed that excessive pressure surgescan occur in the distribution system piping in addition tothe large transmission mains. Walski and colleagues (2004)downplayed the importance of model skeletonization forsystems with relatively small changes in ground eleva-tion and as long as the reduced model size exceeded 10%of the original system. The sample example used in theirstudy, however, assumed that nowater column separation occurs.More recently, other researchershave discouraged the use ofskeletonized models for surgeanalysis of water distributionpiping systems (Boulos et al,2005; Wood et al, 2005b).

Focus of this article. This arti-cle addresses the issues associ-ated with water distributionmodel skeletonization for surgeanalysis. Case studies are pre-sented to demonstrate the sen-sitivity of pressure-surge accu-racy to different levels of modelskeletonization. The authorsshow that model skeletonizationcan introduce significant errorin estimating pressure extremesand can overlook water columnseparation and subsequent col-

lapse at vulnerable locations in the distribution system.These shortcomings can lead to poor design and opera-tion as well as inadequate protection of water distributionsystems and added maintenance costs.

MODEL SKELETONIZATIONModels are only approximations of the real world.

Capturing every component and characteristic of a waterdistribution system is difficult and can result in tremendousamounts of data to manage. Skeletonization is the processof reducing the network model (i.e., producing a skeleton

model) by removing pipesnot considered essential tothe analysis (e.g., pipes withinsignificant carrying capac-ity and pipes that serve rela-tively few customers). Skele-ton models normally includeall hydraulically significantpipes. However, skeletoniza-tion can sometimes have anegative effect on accuracy.

The degree or level ofskeletonization normally depends on the purpose ofthe model, its intended use, and the size and complex-ity of the overall network. Master planning studies(such as long-range capital improvement programdevelopment) may require only pipes with diametersgreater than 12 in. (304.8 mm). Pump stations typi-cally are designed with models of large transmissionmains. Water quality modeling applications normallyrequire a more detailed model to accurately representthe flow and velocity pattern and distribution, espe-cially for identifying localized water quality problem


Before skeletonization After skeletonization 450

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FIGURE 5 Case 2: Transient head profiles at the hydrant

Hea

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Any optimized design that fails to properly accountfor pressure-surge effects is likely to be, at best,suboptimal and, at worst, completely inadequate.


areas. The design of flushing programs (e.g., unidirec-tional flushing) to clean water mains and restore hy-draulic capacity requires comprehensive all-pipe mod-els. Generally, more detailed models result in moreaccurate results and can be used in a wider variety ofapplications (Grayman & Rhee, 2000).

Although there is no national standard for skele-tonization, the US Environmental Protection Agency(USEPA) has issued draft guidance for modeling to sup-port the initial distribution system evaluation (IDSE)under the Stage 2 Disinfectants/Disinfection ByproductRule (USEPA, 2006). The guidance suggests inclusion of

• at least 50% of total pipe length in the distributionsystem;

• at least 75% of the pipe volume in the distributionsystem;

• all pipes 12 in. in diameter and larger;• all 8-in. and larger pipes that connect pressure zones,

influence zones from different sources, storage facilities,major demand areas, pumps, and control valves or areknown or expected to be significant conveyors of water;

• all 6-in. and larger pipes that connect remote areasof a distribution system to the main portion of the system;

• all storage facilities with con-trols or settings applied to governthe open/closed status of the facil-ity that reflect standard operations;

• all active pump stations withrealistic controls or settings appliedto govern their on/off status thatreflect standard operations; and

• all active control valves orother system features that couldsignificantly affect the flow ofwater through the distribution sys-tem (e.g., interconnections withother systems, valving betweenpressure zones).

Modeling of real systemsalways entails an unresolved ten-sion between two elements: howsimply the model can be con-structed and how accurately themodel represents reality. The bestmodels incorporate the best reso-lution between these elements.The modeler must decide on thedesired level of skeletonization fora representative model to produceaccurate results for a particularapplication.

Primary processes of skele-tonization. Skeletonization is theprocess of representing only se-lected pipes in the network modelwhile preserving the operational

performance and integrity of the larger original system. Itconsists primarily of three distinct operations: reduction,hydraulic equivalency, and trimming.

Reduction is the process of removing excessive pipe seg-mentation (caused by valves, fire hydrant, or other data-capture processes) by dissolving interior nodes on pipereaches and combining the associated pipe segments intosingle pipes. For example, the reduction process mightmerge all series pipes of similar characteristics, e.g., diam-eter, material, and age. The merging of series pipes ofsimilar characteristics is an iterative process because manyconsecutive merging levels may exist.

Hydraulic equivalency consists of defining an equiva-lent pipe to replace two or more pipes in parallel or inseries while preserving their carrying capacity. The equiv-alent replacement pipe must produce the same head lossas the original pipes. For series pipes, the same flow mustpass through each pipe in series, and the equivalent pipeis determined as the pipe with the combined length thatwill carry this flow rate and produces the same head lossas the original pipes (sum of all individual head losses). Forparallel pipes, the head loss in each parallel pipe must beequal and is replaced by an equivalent pipe that will trans-


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FIGURE 6 Steady-state analysis before (A) and after (B) skeletonization

Numbers represent the node pressure in psi.

PumpPump

Pump



port the same total flow rate for the same head differenceas the original pipes.

Branch trimming consists of removing dead-end mainsand hydrant leads. Branch trimming is an iterative processbecause many consecutive removal levels may exist.When a pipe segment with a downstream dead-end node(i.e., branch line) is trimmed, the demand at that node

must be shifted to the upstream node of that pipe to pre-serve the total demand in the system. The resultingreduced network is hydraulically equivalent to the largeroriginal model. A comprehensive description of the var-ious model skeletonization operations is provided else-where (Boulos et al, 2006).

PITFALLS OF MODEL SKELETONIZATION FOR SURGEANALYSIS

Skeletonizing water distribution models offers consid-erable benefits in terms of computational performancesuch as a reduction in model complexity, faster modeldevelopment, and shorter run times. However, such amodel reduction process isapplicable only under limitedconditions because networkhydraulic equivalency basis isderived solely from steady-statenetwork equilibrium theory.When applied to steady-statenetwork analysis, the skele-tonized model is able to gen-erate accurate results for flowsand pressures. This theory doesnot hold for surge analysis andshould be limited to steady-state modeling applications.Network model skeletoniza-tion for surge analysis can leadto ineffective design recom-mendations, leaving the systempoorly protected and vulnera-ble to catastrophic failures andcontamination from the exter-nal surrounding environment.

The following discussion highlights some of the diffi-culties inherent in the skeletonization rules outlined pre-viously by identifying where these rules might be mis-leading and how they could lead to a poor basis of design.

Reduction. Merging series pipes (and dissolving interiornodes) may be acceptable in a steady-state analysis,depending on the level of similarity of the pipe charac-

teristics. However, reductionfor surge analysis must bemore carefully assessed.Any differences in the pipesize, material, and thicknessas well as valves, orifices,accumulators, and othersystem elements result inunique transient character-istics. The influences ofthese discontinuities inpipelines create pressure-wave reflections and refrac-tions and significantly influ-

ence both the magnitude and the phase of a rapidpressure pulse during transient conditions. For exam-ple, pipe material doesn’t play any role in steady-stateanalysis; it affects only the pipe roughness coefficient.However, the material elasticity directly affects the wavespeed and significantly influences the magnitude of asurge and the phase of its wave. In addition, theapproach of reallocating nodal demands (when dis-solving interior nodes) during a network reduction appli-cation needs to be carefully considered in surge analysis.It eventually changes the amount and location ofdemands, which can affect the reflection and dissipa-tion of a pressure wave.

Before skeletonization After skeletonization

Time—s

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FIGURE 7 Pump trip transient pressure results at node 1 before and after skeletonization

Skeletonization is the process of representing onlyselected pipes in the network model while preservingthe operational performance and integrity of the largeroriginal system.



Series and parallel pipes. To minimize the number ofpipes in the model, pipes in series and parallel pipes com-monly are replaced by a single hydraulically equivalentpipe with the same carrying capacity of the original pipes.This approach holds true for steady-state analysis with vir-tually no effect on results. However, the hydraulicallyequivalent pipe omits the interaction of wave reflectionsand transmissions in the series and parallel pipes andoften attenuates or magnifies the original surge response.For example, series pipes with area reduction can signif-icantly increase the magnitude of the surge pressure (Wylie& Streeter, 1993), but the hydraulically equivalent pipecannot represent the increase in surge pressure. Similarly,it is not conservative to use the equivalent pipe with theassumption that the parallel pipe configuration can alle-viate water hammer. Other researchers have shown thatsurge response can be more severe in a looped systemthan in a single pipeline (Karney & McInnis, 1990).Depending on system characteristics, the looped systemmay not attenuate a surge pressure and in fact can oftenmake the surge response worse.

Trimming. Branch trimming is widely applied to skele-tonize a large system on the theory that a dead-end main

does not play an important role insteady-state analysis, and thedemand is shifted to the lastremaining node to preserve thetotal system demand. Althoughbranch trimming has no effect onsteady-state flows and pressures,it can significantly affect surgeanalysis. First, the elastic behav-ior of a dead end will be omittedin the trimming process, and thecorresponding wave reflectioncannot be represented. Second, incontrast to open ends or connec-tions to reservoirs where a pres-sure is negatively reflected, a deadend reflects a pressure wave pos-itively, which means that it willexperience the doubling of a surgepressure. For example, when asurge wave of 100 m reaches adead end, that dead end willcause a positive pressure wavereflection of 100 m. Because theincoming and outgoing waves areadditive, the dead end then expe-riences the doubling of the surgepressure, i.e., 200 m. Therefore,dead ends constitute some of themost vulnerable locations forobjectionable pressures andshould be carefully considered ina surge analysis. Additionally,

trimming a dead end overlooks the effect of its ground ele-vation, which, if sufficiently high, may cause cavitationduring a transient episode.

In summary, the traditional rules of steady-state modelskeletonization ignore the complex interaction of tran-sient pressure waves in the different pipe properties andcharacteristics of a water distribution system. Thehydraulic equivalency theory used in model skele-tonization and derived from steady-state network equi-librium is not applicable to surge analysis. At pipe junc-tions and dead ends, wave reflections and transmissionsoccur, which often magnify or attenuate the surge waves.Conducting a surge analysis with a skeletonized modelmay not be conservative and may be unsuitable for esti-mating transient pressure extremes in a distribution net-work system.

CASE STUDIESThe case studies cited here provide an opportunity to

examine the rules of skeletonization and compare surgeanalysis results for original and skeletonized models. Inparticular, these studies illustrate the pitfalls of steady-state model skeletonization for surge analysis. All transient

Pump tripMeasurement location (node 242)

FIGURE 8 A network system before skeletonization

Pump tripMeasurement location (node 242)

FIGURE 9 A network system after skeletonization



modeling results presented here can be obtained usingthe eigenvalue approach (Jung & Karney, 2004a), themethod of characteristics (Wylie & Streeter, 1993), orthe wave characteristic method (Boulos et al, 2006; Woodet al, 2005a) and can be reproduced using available com-mercial or in-house water hammer codes.

Case 1: A small water pipeline system. The first case studyuses the small water pipeline system shown in Figure 1.This system consists of a 200-m (656.2-ft) head reservoirfeeding a network of five pipe sections and four junctions.Each pipe has a diameter of 1 m (3.3 ft), length of 1,000m (3,280.8 ft), Hazen-Williams roughness coefficient of100, and wave speed of 1,000 m/s (3,280.8 fps). The ele-vation of each junction is assumed to be 0 m. Junction J4designates a dead end with no external demand. Termi-nal junction J1 has a demand of 1 m3/s (35.3 cfs). A rapiddemand decrease over a 1-s time period is initiated to intro-duce a transient condition.

In this case study, three levels of skeletonization aredemonstrated. For the first level, parallel pipes P1 andP2 are replaced with a hydraulically equivalent pipe(P12) that has the same length and roughness coefficientof the original pipes but an equivalent diameter of1.302 m (4.272 ft). Second, the series pipes P3 andP12 are replaced with an equivalent pipe that has thesame roughness coefficient of the original pipes but itsequivalent diameter andlength are 1.096 m (3.596ft) and 2,000 m (6,561.7ft), respectively. For thefinal skeletonization level,the dead-end junction J4and pipe (branch) P5 areremoved. According to thehydraulic equivalency the-ory, each of the three dis-tinct skeletonized modelsproduces the same steady-state hydraulic results asthe original system. Theresulting skeletonized system consists of one reservoirfeeding two pipes in series.

Figure 2 shows the transient head profiles at junctionJ1 for the three levels of skeletonization. Because theskeletonized models cannot represent the reflections andtransmissions of the pressure waves at the original dis-continuities, as the degree of skeletonization increases,the transient response becomes more severe, comparedwith the original system. The figure also shows that thephase of the original surge wave and its magnitude hasbecome deformed and thus can mislead the preset sched-ule of a surge protection device (e.g., surge anticipationvalve) in the skeletonized model.

Figure 3 shows the maximum and minimum headsand their corresponding locations according to the dif-ferent degrees of skeletonization. After the skeletoniza-

tion of the parallel and series pipes (first and secondskeletonization levels), the surge response becomes worsethan in the original system because the maximum headsof the skeletonized models are higher and the minimumheads are lower. The skeletonization of the dead endprovides less severe transient response than the secondlevel skeletonization. For this case study, the paralleland series pipes attenuated the transient wave, but thedead end magnified it. So the reflective question wouldbe “Does skeletonization make transient responsesappear to be more or less dangerous?”

Case 2: Cavitation in a dead end. Another possiblepitfall of model skeletonization is the elimination of theunique characteristics of the system components.Although a dead end located at high elevation can beeasily removed in the skeletonization process, thisremoval can lead to a possible cavitation problem dur-ing transient conditions. If a negative surge is propa-gated to the dead end and its local pressure is low-ered to the vapor pressure, all gas within the water isgradually released, and the water starts to evaporate.When the pressure recovers, water enters the cavityand collides with the gases, resulting in a large pres-sure-surge spike.

The second case study uses the small water pipelinesystem shown in Figure 4. This system consists of a 130-

m (426.5-ft) head reservoir feeding a network of threepipe sections and three junctions. The properties of eachpipe section are identical to those used in case 1, but adead-end pipe is installed vertically 20 m (65.6 ft) fromthe main pipeline. The terminal junction J1 has a steadydemand of 0.1 m3/s (3.53 cfs) and a fire-flow demand of1 m3/s (35.3 cfs). It is assumed that the fire flow is initi-ated in 0.1 s. In the skeletonization process, the dead-endpipe is removed from the main pipeline. This case studyillustrates the role of a dead end in surge analysis duringa fire flow startup.

Figure 5 shows the transient head profiles at thehydrant (J1) with and without the dead end. In theoriginal system, the local transient pressure at the deadend is lower than the vapor pressure, thus causing cav-itation. The transient head profile after skeletoniza-

A comprehensive surge analysis should be performedon a representative network model of the distributionsystem to properly locate and size the most effectivecombination of surge-protection devices.



tion (removal of the dead end) shows less severe tran-sients without any cavitation. The cavitation in theoriginal system makes the transient response worse;the maximum heads before and after skeletonizationare 434.5 m (1,425.5 ft) and 245.9 m (806.8 ft),respectively. A similar case may result from the paral-lel- and series-pipes skeletonization process. By com-bining the parallel and series pipes into an equivalentpipe, the high elevation areas in the original systemcould be eliminated, and the presence of potential cav-itation could be overlooked.

Although case 2 illustrates a single dead end, the studycan easily be extended to a separate subnetwork con-nected to the main distribution system. The subnetworkmay potentially be eliminated in the skeletonizationprocess by shifting all node demands in the subnetworkto their associated upstream nodes; however, this skele-tonization would ignore the potential for cavitation in thesubnetwork. Additionally, dead ends lock pressure wavesinto the system in a cumulative fashion and will doublea surge pressure, making the system even more vulnera-ble to cavitation.

Case 3: A network system. In order to show some ofthe shortcomings of skeletonization for surge analysisin a larger, more complex system, the rules of modelskeletonization were applied to a water distribution net-work studied by other researchers (Rossman, 2000). Thisnetwork is shown in Figure 6, part A, along with itssteady-state hydraulic results. Figure 6, part B, showsthe skeletonized model and its steady-state results aftertrimming dead-end pipes and replacing series and parallelpipes with hydraulically equivalent pipes. For this exam-ple, a transient is introduced from a pump trip initiated2 s after steady-state equilibrium.

Figure 7 shows the transient head profiles at node 1before and after skeletonization. In contrast to case 1, thetransient results for the skeletonized model are less severethan those of the original system. The maximum surgeheads before and after skeletonization are 161 m (528 ft)and 131 m (430 ft), respectively. Thus, the maximumsurge head of the original model is 23% higher than thatof the skeletonized model.

Case 4: An actual network system. To highlight someof the pitfalls of skeletonization for surge analysis on alarger, more complex system, the rules of model skele-tonization were applied to an actual water distributionnetwork (Figure 8). This system comprises 1,639 junc-tions, 2,088 pipes, 23 wells, 23 pumps, and one storagetank. The identity of the corresponding water utility iswithheld because of security concerns.

Figure 9 shows the skeletonized model after trim-ming dead-end pipes and replacing series pipes withhydraulically equivalent pipes while conserving totalsystem demand. The skeletonized network, now reducedto 1,134 pipes and 685 junctions, meets the USEPAIDSE network model guidelines (USEPA, 2006). Forthis example, a transient condition is triggered by pumptrips initiated at 5 s. Figure 10 shows the transient headprofiles at junction 242 before and after skeletoniza-tion. As shown in the figure, the transient results for theskeletonized model are much less severe than those forthe original system. Satisfying the hydraulic equiva-lency principle, both the original and skeletonized mod-els produce the same steady hydraulic equilibrium con-dition (66.6 m or 218 ft) for the initial 5-s period.However, the maximum surge heads before and afterskeletonization are 153.1 m (502.3 ft) and 84.7 m(277.9 ft), respectively. Thus the maximum surge head

of the original model is 81%higher that that of the skele-tonized model. This exercisedemonstrates some limitationsof the IDSE hydraulic modelguidelines for transient analysis.For example, the IDSE guide-lines do not consider the impor-tance of dead ends and high ele-vation points in the distributionsystem, both of which may sig-nificantly affect pressure surges.

Overdesign versus underdesign.The transient response of a skele-tonized model can be more or lesssevere than that of the originalmodel, but it is difficult to accu-rately predict if the transientresults of a skeletonized modelwill be more or less conservative.Transient results are stronglydependent on the system charac-

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FIGURE 10 Pump trip transient results at node 242

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teristics as well as the level of skeletonization. The moreconservative case may result in overdesign of surge sup-pression and protection devices, yet overdesign doesn’tnecessarily indicate a higher degree of safety unless allhydraulic transient conditions have been properly ana-lyzed. An overdesigned system may sometimes be worsethan an underdesigned one because the overdesignedhydraulic devices themselves could deteriorate the system’ssurge response (Jung & Kar-ney, 2006; Karney & McIn-nis, 1990). On the otherhand, the less-conservativeresults may lead to under-design of surge suppressionand protection devices, leav-ing the system vulnerableduring surge conditions.Both overdesigns and under-designs can place the distri-bution system at risk. Engi-neers must carefullyconsider all potential dan-gers for their system designs and estimate and eliminatethe weak spots. They should then embark on a detailedtransient analysis in order to make informed decisions onhow to best strengthen their systems and ensure safe,reliable, and economical operations.

CONCLUSIONSRecent concerns about protecting water distribution

systems from potential intrusion of contaminants attrib-utable to low- or negative-pressure conditions haveunderscored the importance of surge modeling to controlobjectionable hydraulic transient pressures. Traditionally,surge modeling has focused on analyzing large-diametertransmission mains with few or no branches and loops.Skeletonization techniques derived from hydraulic equiv-alency theory have been used to reduce the size and com-plexity of these systems and generate smaller skeletonizedmodels. Because of branches and loops, however, dis-tribution systems respond differently than transmissionlines, and excessive pressure surges can be present indistribution piping. The rules of skeletonization ignorethe inherent problem of interaction of the surge wavesin different components and the pipe properties of awater distribution system. At pipe junctions and dead-end branches, wave reflections and transmissions occur,which often magnify or attenuate the impinging surgewaves. Furthermore, wave speed is a function of pipematerial, diameter, and thickness. A surge analysis canbe used to accurately determine the extent of transientpressure extremes but only if detailed representativemodels are used.

Proper system design, operation, and maintenancecan help water utilities achieve a high degree ofhydraulic integrity and reliability and extend the life of

their water distribution systems. This requires an accu-rate prediction of the system’s worst-case performanceunder all hydraulic transient conditions. Transientresponse is highly sensitive to the system-specific char-acteristics, and a skeletonized model can yield incorrectresults, which in turn can lead to poor design and insuf-ficient surge protection. Surge analysis on detailed mod-els is becoming common practice, thanks to the rapid

development of fast computers and numerical solutionschemes that are both powerful and highly efficient.Properly defined models can be used to effectively esti-mate intrusion potential, identify susceptible regionsin the distribution system that are of greatest concernfor vulnerability to objectionable (low or negative)pressure surges, and evaluate how they can be avoidedand/or controlled (Boulos et al, 2006; 2005).

Effective management strategy may dictate theinstallation of surge tanks at pump stations (to dampennegative pressure waves) and other surge-controldevices at vulnerable system locations such as highpoints. These surge-control devices may be cost-pro-hibitive, but they offer the only practical opportunityto protect the public from potential intrusion of con-taminants via low- or negative-pressure developments.No two water distribution systems are hydraulicallyidentical, however, and therefore no general rules orguidelines are universally applicable for eliminatingtransient pressures in water distribution systems. Anysurge-protection devices and/or operating strategiesmust be chosen accordingly.

The final choice should be based on the initial causeand location of the transient disturbance(s), the sys-tem itself, the consequences if remedial action is nottaken, and the cost of the protection measures them-selves. A combination of devices may prove to be themost effective and most economical. A comprehensivesurge analysis should be performed on a detailed rep-resentative network model of the water distributionsystem in order to determine, locate, and size the mosteffective combination of surge protection devices andthus ensure safe and economical operation and pro-tect public health.

Transient results are strongly dependenton the system characteristics as well as thelevel of skeletonization.



ABOUT THE AUTHORSBong Seog Jung is a professional engi-neer with MWH Soft in Arcadia, Calif.He has BS and MS degrees in environ-mental engineering from PusanNational University in Pusan, SouthKorea, and a PhD in civil engineeringfrom the University of Toronto inOntario. For the past eight years, his

research and consulting experience has focused onhydraulic transients and optimization of distributionsystems. Paul F. Boulos (to whom correspondence

should be addressed) is the president and chief operat-ing officer of MWH Soft, 380 Interlocken Crescent,Ste. 200, Broomfield, CO 80021; e-mail [email protected]. Don J. Wood is professor emeritusin the Department of Civil Engineering at the Univer-sity of Kentucky in Lexington.

If you have a comment about thisarticle, please contact us at

[email protected].

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Pitfalls of water distribution model skeletonization for surge analysis.

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