wdsa2006 efficientpdd haestad eng lowres

7/27/2019 WDSA2006 EfficientPDD Haestad Eng Lowres

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8 th Annual International Symposium on Water Distribution System Analysis, Cincinnati, Ohio, August 27-30, 2006

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EFFICIENT PRESSURE DEPENDENT DEMAND MODEL FOR LARGEWATER DISTRIBUTION SYSTEM ANALYSIS

Zheng Yi Wu Email: [email protected]

Rong He Wang Email: [email protected]

Thomas M. Walski Email: [email protected]

Shao Yu Yang Email: [email protected]

Daniel Bowdler Email: [email protected]

Haestad Methods Solution Center, Bentley Systems, Incorporated27 Siemon Co Dr. Suite 200W

Watertown, CT06795, USAChristopher C. Baggett

Jones, Edmunds & Associates, Inc.730 NE Waldo Road

Gainesville, FL 32641, USA Email: [email protected]

Abstract

Conventional water distribution models are formulated under the assumption that water consumption or demand defined at nodes is a known value so that nodal hydraulic head and pipe flows can be determined by solving a set of quasi-linear equations. This formulation is well developed and valid for the scenariosthat the hydraulic pressures throughout a system are adequate for delivery the required nodal demand. However, there are some scenarios where nodal pressure is not sufficient for supplying the required demand. These cases may include the planned system maintenances, unplanned pipe outages, power failure at pump stations, and insufficient water supply from water sources. In addition, some water consumptions like leakages are pressure dependent. In this paper, a robust and efficient approach for pressure dependent demand analysis is developed for simulating a variety of low pressure scenarios. Aset of element criticality evaluation criteria is also proposed for quantifying the relative importance of theelements that may be out of service. The results are presented for the applications of the approach to thetrivial systems and also to a large water system. It is demonstrated that great modeling performance and convergence rates are achieved for modeling pressure dependent demand conditions and evaluating theelement criticality of the large water distribution systems.

Key WordsHydraulic model, water distribution system, pressure dependent demand, pressure deficient condition,criticality, reliability

INTRODUCTION

A water distribution model is created by using a link-node formulation that is governed by twoconservation laws, namely mass balance at nodes and energy conservation around hydraulic loops. Thenode is a point where water consumption is allocated and defined as demand, which is treated as a knownvalue so that nodal hydraulic head can be solved. This formulation is valid only if the hydraulic pressuresat all nodes are adequate so that the demand is independent of pressure. It is also valid approach foranalyzing volume-based demand such as filling bath tub, flushing toilet etc. even under low pressure
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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conditions. However, in many cases nodal pressure is not sufficient for supplying the desired demand.These cases may include the planned system maintenances, unplanned pipe outages, power failure atpump stations, and insufficient water supply from water sources.

Water companies are required to constantly evaluate the level of water supply while coping withemergency events. A tentative guideline requirement is that a water system must meet a certain level of the original demand for the majority of customer and no large group of customers should receive theiroriginal demand. For instance, UK water companies are required by law to provide water at a pressurethat will, under normal circumstances, enable it to reach the top floor of a house. In order to assess if thisrequirement is satisfied, companies are required to report against a service level corresponding to apressure head of 10 meters (14.2 psi) at a flow of 9 liter per minute (2.4 gpm). In addition, watercompanies are also required to report the supply reference for unplanned and planned serviceinterruptions.

Water asset management has become an ever-increasing task for water utilities. It requires acomprehensive evaluation of above and underground facilities including every pipeline segment in awater system. The impact of each pipe segment needs to be carefully quantified and thus it forms arational basis for asset management plan. The impact evaluation is usually undertaken by performing the

hydraulic analysis under the assumption that a pipe or a number of pipes is out of service, namelydisconnected from a system, which is likely to cause pressure deficient conditions. The accurate analysiscannot be achieved without considering the impact of the pressure change on the flow supplied.

Some methods in literature proposed for modeling pressure deficient demand (Jowitt and Xu 1993; andGupta and Bhave 1996). None of the methods seems to consider the transition between the pressuresufficient and deficient conditions. Ang and Jowitt (2005) took a modeling approach by adding anartificial reservoir at every pressure deficient node and removing it from fixed demand nodes in aniterative procedure, which requires numerous repeat solutions of the system equations with no guaranteeof convergence. The iterative calculation stops until correct pressure sufficient nodes are identifiedwithout negative pressure at a node. This method seems to avoid introducing extra parameters like themethod based upon orifice flow equation. But it can be difficult to apply this method to a large water

system, because it is computationally expensive to add a virtual reservoir to each of hundreds of thousands of nodes and then shuffle them around. It can be also programmatically difficult to implementit since each iteration will require changing the solution matrix.

Alternative, the modeler may model pressure dependent demand by using emitter at a node asimplemented in EPANET2 (Rossman, 1994). Unfortunately, the emitter function produces negativedemand whenever and wherever a nodal pressure becomes negative. This is not the case in real worldunless the outlet is submerged in a tank. The fact is that demand is zero when the pressure becomes equalto or less than zero. There is also no upper limit for emitter flow. In other words, the emitter flow canincrease without bound as the pressure increases. Consequently, the high pressure node would draw morewater than the relatively low pressure locations, which distorts the actual supply because in most cases noextra demand or consumption would be required as long as the pressure is above certain desired

threshold.

To effectively model nodal demand as a function of nodal pressure, a robust and efficient approach of pressure dependent demand model (Wu and Walski 2006) has been developed and integrated into themodeling framework WaterGEMS v8 (Bentley 2006).


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PRESSURE DEPENDENT DEMAND

When an outage occurs, nodal pressures are affected. Some locations may not have the sufficientpressure. Pressure may drop below a reference level, so-called reference pressure for supplying 100% of desired demand or reference demand. Whenever the pressure is below the reference pressure, nodaldemand, the water available at a location, is certainly dependent on the pressure at the node. In other

words, unlike the conventional approach of demand-driven analysis, demand is a function of pressure inpressure dependent demand (PDD). However, it is believed that a junction demand is not affected bypressure or water consumption will be maxed out (keep constant) if the pressure is above a threshold. Ingeneral, the threshold above which demand is no longer sensitive to pressure must be greater than orequal to the reference pressure at which all demand is met. The junction demand is reduced from thenormal reference demand when the pressure is dropping below the reference pressure and increased abovereference demand when the pressure is greater than the reference pressure but less than the threshold.

PDD is then defined as follows.


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0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Percent of Pressure Threshold

P e r c e n t o f R e f e r e n c e D e m a n d

Figure 1 A Typical Pressure Dependent Demand Curve

SOLUTION METHODOLOGY

The key solution methodology is how to solve for the pressure dependent demand as given by Eq.(1).Conventionally, nodal demand is a known value. Applying the mass conservation law to each node andenergy conservation law to each loop, the network hydraulics solution can be obtained by iterativelysolving a set of linear and quasi-nonlinear equations. A unified formulation for solving network hydraulics is given as global gradient algorithm (GGA) as (Todini 1988):

=

dq

dE

dH

dQ

D A

A D......

...

............

2221

1211

(2)

The only difference from the original GGA is the new diagonal matrix D22 , which is the deviation of A22of pressure head H . For supply characteristic defined as Eq.(1), the corresponding expression is


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Where j denotes the pipe j that is connected with node i. This notation is the same as EPANET2implementation.

The PDD approach as formulated above can be applied to analyzing pressure deficient of many scenariosincluding element outages, system maintenance, leakage, insufficient water sources, intermittent supply,sprinkler flows, reliability and criticality analysis.

Criticality Analysis

Criticality analysis is to evaluate the impact of elements outage. Instead of considering each pipe outageas defined in a model, a more practical approach is undertaken by dividing a system into a number of segments (Walski 1993) isolated by all the valves, each of which represents a smallest isolable portion of the system. The impact of the segment is evaluated by performing a hydraulic model simulation with thesegment out of service. A number of indicators can be used to assess the criticality of the segments asfollows.

1. System supply shortfall under steady state simulation;2. System supply shortfall percentage;3. Accumulated system supply shortfall over an extended period of time4. Percentage of accumulated system supply;5. Node with maximum demand shortfall.

For a given outage, there are three cases for any node:1. No effect on pressure (or demand)2. Node is completely cut off from water source (demand supplied = 0)3. Demand is reduced because pressure drops (demand = F(pressure))

PDD calculations are required in the third case.

APPLICATIONS

Three examples are presented below to illustrate the application of pressure dependent approach. The firstexample is taken from the literature (Gupta and Bhave 1996; and Ang and Jowitt 2005), the secondexample is to demonstrate the PDD application to criticality analysis and the third example is toexemplify the efficiency of the integrated approach applied to a large water system.

Example 1: Benchmark System

This example system is as in Figure 2. It consists of one source tank, 4 demand nodes and 4 pipes inseries. The trivial system was used by a few researchers for testing the methods of pressure deficienthydraulic analysis. Under the normal condition, the system supply adequate pressure for the desireddemand. The pressure deficient condition is caused by a big fire flow of 3.00 m 3 /min at node J-4.Hydraulic results are given for both scenarios by using conventional demand-driven analysis approach.

Conventional analysis shows that the pressure at J-3 significantly drops to almost zero, but the demand isstill met. A pressure dependent demand approach is applied to analyze the system.


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Figure 2 Series system for testing pressure dependent demand analysis

Table 1 Conventional hydraulic simulation results with tank level of 109.86 meters

J-1 J-2 J-3 J-4

ScenariosQ

(m 3 /min)P

(m)Q

(m 3 /min)P

(m)Q

(m 3 /min)P

(m)Q

(m 3 /min)P

(m)

Base 2 17.13 2 16.1 3 11.08 1 15.83Base and fire flow 2 14.97 2 10.55 3 0.02 4 1.98

While applying the pressure dependent demand approach to analyzing the system under the fire flow at J-4, two scenarios are considered as follows.

Scenario I: all the nodal demands including fire flow at J-4 are considered as pressure dependentdemand;

Scenario II: fire flow at J-4 is considered as volume-based demand while the other demands aretreated as pressure dependent demand. This is because fire truck may pump whatever is available

from the tank regardless the pressure at hydrant.

Table 2 Simulation results of 100% pressure dependent demand for different source heads

J-1 J-2 J-3 J-4Tank level

(m)Q

(m 3 /min)P

(m)Q

(m3 /min)P

(m)Q

(m 3 /min)P

(m)Q

(m3 /min)P

(m)109.86 1.95 16.29 1.86 13.93 2.32 6.57 3.13 9.64100.00 1.37 8.03 1.37 7.58 1.45 2.59 2.53 6.2898.78 1.28 7.01 1.30 6.80 1.31 2.11 2.44 5.8996.82 1.12 5.38 1.18 5.57 1.06 1.37 2.31 5.2691.97 0.58 1.42 0.81 2.66 0.00 0.00 2.01 3.9791.03 0.38 0.60 0.70 1.97 0.00 0.00 1.88 3.4789.08 0.00 0.00 0.36 0.51 0.00 0.00 1.57 2.4385.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


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Table 3 Simulation results of mixed volume-based demand and pressure dependent demand for differentsource heads

J-1 J-2 J-3 J-4Tank level

(m)Q

(m 3 /min)P

(m)Q

(m3 /min)P

(m)Q

(m 3 /min)P

(m)Q

(m3 /min)P

(m)109.86 1.94 16.08 1.83 13.36 2.09 5.36 3.70 7.73100.00 1.35 7.79 1.32 6.94 0.99 1.21 3.49 3.8498.78 1.26 6.79 1.24 6.20 0.80 0.79 3.47 3.4596.82 1.10 5.19 1.12 5.04 0.42 0.22 3.43 2.9391.97 0.27 0.31 0.52 1.10 0.00 0.00 3.13 0.2691.03 0.27 0.31 0.52 1.10 0.00 0.00 3.13 0.2689.08 0.00 0.00 0.00 0.00 0.00 0.00 3.00 0.0085.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Both scenarios are simulated for different available source heads or tank levels, which give different

hydraulic grades and pressures at nodes. The pressure dependent demand analysis is undertaken by usingthe corresponding nodal pressures under normal condition (Base scenario) given as in Table 1 asreference pressures as in Eq(1) for each node and a large value as pressure threshold. This effective meansthat the normal nodal demands (without fire flow at J-4) are met at the normal pressure conditions. Underthe fire flow conditions, the pressure dependent demand analysis results are given in Table 2 and 3 for100% PDD and the mixed PDD and volume-based demand.

When all the nodal demands are treated as PDD, Table 2 shows that the demands including fire flowdecrease as the pressures at nodes decrease. The predicted demand is zero (0.0) when the pressurebecomes zero or tank runs out of water. If the fire flow is treated as volume-based demand and the otherdemands are modelled as PDD, Table 3 illustrates that the fire flow is always met when there is wateravailable from the source (tank T-1), and that the pressure dependent demands change as pressure

changes.

This example shows that the method developed can effectively simulate scenarios of pressure deficientconditions same as Ang and Jowitt s approach. The method is better than the previous method insimulating the combination of pressure-dependent and volume-based demands at the same node andpredicting the partial nodal demand when the pressure is between the desired or reference pressure andzero.

Example 2: Small System

This is a simple example system as shown in Figure 2, supplied by a reservoir via a pump and a storagetank in north. The system is used to demonstrate the criticality analysis with and without pressure

dependent demand.Criticality analysis is undertaken in two steps. First step is to perform the system segmentation thatdivides the system into a number of segments, as shown in Figure 4. A hydraulic simulation is conductedfor one segment by assuming that all the elements (pipes and nodes) are out of service. The outage impactis evaluated by system supply shortfall as given in Table 4 and 5.


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Figure 3 System layout of example 2 with isolation valves for criticality analysis

Criticality analysis results, as shown in Table 4, indicate that most of the segments outage cause systemsupply shortfall by the conventional demand-driven analysis, the maximum demand shortfall may go upabout 70%. When a segment is out of service, the flow path will change accordingly, which may result inlarge head loss so that negative nodal pressures may occur by conventional demand-driven analysis. Forinstance, when either segment s4 or s5 is out of service, the system demand will be supplied by only oneflow path via s12 or s8, since the demand-driven analysis assumes that the nodal demand is known andindependent from the pressure so that 100% of demand for the rest of system will be forced through theremaining connected pipeline, thus a huge head loss is resulted in along the pipelines and negativepressures will occurs at the downstream nodes, where the demand is deemed not met, therefore a largerthan expected demand shortfall is reported for s4, s5 and s12 as shown in Table 4.

Figure 4 Color coded segmentation of the example system for criticality analysis


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Table 4 Criticality analysis results under steady state simulation

Conventionaldemand-driven

simulation

PDD simulation withreference Pressure of

20 psi


100 psi

Segments

SystemFlow(gpm)

SystemSupplied

Flow(gpm)

SystemDemandShortfall

(-) orSurplus(+) %

SystemSupplied

Flow(gpm)


(-) orSurplus(+) %

SystemSupplied

Flow(gpm)


(-) orSurplus(+) %

S-1 670.8 670.8 0.0 670.8 0.0 670.8 0.0S-2 670.8 670.8 0.0 659.7 -1.7 452.7 -32.5S-3 670.8 477.4 -28.8 477.4 -28.8 465.6 -30.6S-4 670.8 200.4 -70.1 541.8 -19.2 481.1 -28.3S-5 670.8 114.2 -83.0 480.8 -28.3 366.8 -45.3S-6 670.8 598.2 -10.8 598.2 -10.8 561.1 -16.4

S-7 670.8 537.8 -19.8 537.8 -19.8 460.8 -31.3S-8 670.8 608.4 -9.3 591.7 -11.8 478.5 -28.7S-9 670.8 668.8 -0.3 668.8 -0.3 668.8 -0.3

S-10 670.8 639 -4.7 639.0 -4.7 566.4 -15.6S-11 670.8 632.2 -5.8 632.2 -5.8 561.5 -16.3S-12 670.8 228.0 -66.0 493.3 -26.5 421.6 -37.2S-13 670.8 583.8 -13.0 583.8 -13.0 499.8 -25.5S-14 670.8 670.8 0.0 659.7 -1.7 452.7 -32.5

Using pressure dependent demand simulation, the impact of each segment is analyzed by assumingdifferent reference pressure of 20 psi and 100 psi. The results obtained are given in Table 4 and Table 5for both steady state and extended period simulations. Instead of forcing all the required demand through

the connected flow path, the nodal demand is calculated by the available pressure accordingly by the PDDfunction definition. Therefore, available partial demand is more accurately calculated for node, the systemshortfall is estimated less than the demand-driven approach.

The greater the reference pressure, i.e. 100 psi, the less demand is supplied at the same pressure level, thegreater demand shortfall is resulted in as indicated in Table 4. The criticality results for EPS simulation,as shown in Table 5, show the impact of each segment out of service for 24 hours. More segments areidentified to cause the system shortfall with greater supply shortfall. The critical segments are s-2, s-5 ands-14 that connect to the reservoir via the pump, and also s-12 that represents the weakest distributionsegment that causes the greatest pressure drop when the outage occurs.

In addition, the reference pressure appears to be an important parameter for applying pressure dependent

demand in general, and evaluating the criticality using pressure in particular. The reference pressure maybe different from one type customer to another (such as residential, commercial and industry), but, it isnot hard to come up with a rational pressure required for deliver the desired water supply service for aparticular type of water customers.


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Table 5 Criticality analysis results under extended period simulation

Conventionaldemand-driven

simulation


20 psi


100 psi

Segments

SystemFlow

Volume(MG)

SystemSuppliedVolume

(MG)


(-) orSurplus(+) %


(MG)


(-) orSurplus(+) %


(MG)


(-) orSurplus(+) %

S-1 0.96 0.97 0.00 0.97 0.0 0.97 0.0S-2 0.96 0.09 -90.90 0.09 -90.4 0.09 -90.9S-3 0.96 0.69 -28.80 0.69 -28.8 0.64 -33.5S-4 0.96 0.29 -70.50 0.76 -21.6 0.69 -28.3S-5 0.96 0.02 -98.40 0.09 -90.9 0.09 -90.9S-6 0.96 0.86 -10.80 0.86 -10.9 0.78 -19.2

S-7 0.96 0.70 -27.90 0.73 -24.3 0.63 -34.5S-8 0.96 0.80 -17.60 0.80 -17.5 0.66 -31.2S-9 0.96 0.96 -0.30 0.96 -0.3 0.96 -0.3

S-10 0.96 0.89 -8.30 0.90 -7.1 0.79 -18.6S-11 0.96 0.91 -5.80 0.90 -7.1 0.78 -19.2S-12 0.96 0.28 -70.60 0.66 -31.6 0.58 -40.3S-13 0.96 0.83 -13.90 0.82 -15.2 0.69 -28.1S-14 0.96 0.09 -90.90 0.09 -90.6 0.09 -90.9

Example 3: Large System

This example, as shown in Figure 5, is a real water system of Pinellas County in Florida. The watersystem supplies drinking water to approximately 800,000 customers along Florida s central west coastand is sourced from Tampa Bay Water (TBW), the region s wholesale provider. Hydraulically, thesystem functions as two large transmission and distribution systems of the Northern system and theCentral/Southern system that are networked together with a variable interface location, depending ondemand conditions. Water source of the Northern system is from the Eldridge Wilde Wellfield. Watersource of the Central/Southern system is from a 66-inch pipeline that connects directly to the TBWsystem which contains blended water including desalted water, surface water, and groundwater.

The system is composed of an extensive piping network, six pumping stations, and 11 storage tanks. Thepiping network includes approximately 2,000 miles of piping, with diameters ranging from less than 1-inch to 66-inch and with several pipe materials including ductile iron, gray cast iron, pre-stressed concretecylinder, steel, and polyvinyl chloride. The six pumping stations include 25 constant-speed and variable-speed pumps.

The model of the water system consists of 80,870 pipe, 25 pumps, and 11 storage tanks. The model hasbeen constructed for Pinellas County by Jones, Edmunds & Associates, Inc. in support of a blending andpumping facility with a design maximum daily demand capacity of approximately 100 million gallons perday. The new facility will blend the source waters and distribute a consistent water quality to theCounty s customers.


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To test the application of applying pressure dependent demand to criticality analysis based uponsegmentation, more than 69,921 isolation valves were automatically inserted onto to the pipelinesprogrammatically. This allows network tracing algorithm to automatically generate 65,562 segments forthe whole system. The criticality analysis is performed for each of the segments, that is 65,562consecutive hydraulic runs automatically conducted for each of the conventional demand-driven andpressure dependent demand simulations. Each of which took about 2 hour 58 minutes and 20 seconds,and 5 hours 33 minutes and 20 seconds respectively on a Pentium 4 machine with CPU 3.06 GHz and 1.0GB of RAM. In average, each steady state hydraulic run takes about 0.2 seconds and 0.3 seconds for thedemand-driven and PDD simulation respectively. It exemplifies the efficiency of the hydraulic simulationof both conventional demand-driven and pressure dependent demand analysis for this scale of the model.

The criticality analysis results obtained so far are based on the hypothetic isolation valve locations. Oncethe real valve data is ready, the model building tool in WaterGEMS v8 can automatically insert theisolation valves into the model for more accurate analysis. This excise proves the robustness andefficiency of the integrated network segmentation, criticality analysis and pressure dependent demandmodeling.

Pressure dependent demand analysis is able to more accurately quantify the impact of pipe outage. For

instance, Figure 6 shows the northern part of Pinellas water system, a pipeline is identified critical to thenode WSMB and also the nodes in the west of WSMB. Under normal condition, the nodal demand is metat the pressure of 60 psi, as shown in Figure 7. It is noticed that any of the pipes along the critical segmentis out of service, it will cause a dramatic pressure drop. Using conventional demand-driven analysis, thecalculated demand is met as requested, but the calculated pressure at WSMB goes more than -70 psi asshown in Figure 8. It is just not possible to supply the full demand under the negative pressure. Theavailable demand needs to be predicted for such an outage event.

To predict how much water can be supplied under such a pressure deficient condition, pressure dependentdemand analysis is applied with a reference pressure specified as the normal operating pressure of 60 psi,and the pressure threshold set to be equal to the reference pressure, a power PDD function, given asEq.(1) with exponent of 0.5, is used for PDD simulation run. The results are illustrated in Figure 9. The

available demand is reduced accordingly as pressure drops. This exemplifies that PDD analysis is able torationally evaluate the impact of pipe outage while conventional demand-driven analysis may lead toconfusing results.

CONCLUSIONS

The pressure dependent demand analysis approach developed in this paper has provided a robust andefficient method for analyzing many conditions where the demand is function of pressure in a waterdistribution system. It proves to be flexible at modeling the mixed volume-based and pressure dependentdemands, which improves the modeling capability of the conventional network hydraulic analysis. Theapplication of the pressure dependent demand to criticality analysis enables engineers to practicallyevaluate the system impact than using the conventional demand-driven analysis method.

REFERENCES

Ang, W. H. and Jowitt, P.W. (2006) Solution for Water Distribution Systems under pressure-deficientconditions ASCE J. of Water Resour. Plan. Manage ., 132(3), 175-182.

Bentley Systems, Incorporated, (2006). WaterGEMS v8 User Manual. 27 Siemon Co Dr, Suite200W,Watertown, CT06795, USA.

Gupta, R. and Bhave, P. R. (1996) Comparison methods for predicting deficient-network performance.

ASCE J. of Water Resour. Plan. Manage ., 122(3), 214-217.


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Jowitt, P. W. and Xu, C. (1993). Predicting pipe failure effects in water distribution systems. ASCE J.of Water Resour. Plan. Manage ., 119(1), 18-33.

Rossman, L.A. (1994). EPANET Users Manual. Drinking Water Research Division, Risk ReductionEngineering Laboratory, Office of Research and Development, U.S. Environmental ProtectionAgency, Cincinnati, Ohio. USA.

Todini, E. & Pilati, S. (1988). A gradient algorithm for the analysis of pipe network. In Coulbeck B. andChun-Hou O. (eds). Computer Applications in Water Supply, Vol. 1 System Analysis and Simulation, John Wiley & Sons, London, pp.1-20.

Walski, T.M. (1993), Water Distribution Valve Topology, Reliability Engineering and System Safety ,Vol. 42, No. 1, p. 21.

Wu, Z. Y. and Walski, T. M. (2006) Pressure Dependent Hydraulic Modelling for Water DistributionSystems under Abnormal Conditions , Proc. of IWA World Water Congress, Sept.10-14, 2006,Beijing, China.

Figure 5 Hydraulic model layout for Pinellas county water system


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Figure 6 Northern part of Pinellas water distribution system an example of critical pipelineand demand shortfall nodes caused by critical pipeline outage

Demandshortfallnode:WSM B

CriticalPipes


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Figure 7 Calculated demand and pressure of node WSMB under normal operating condition(without pipe outage)

Figure 8 Calculated demand and pressure at node WSMB by using demand-driven analysisunder the critical pipe outage


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Figure 9 Calculated available demand, pressure and demand shortfall at node WSMB by usingpressure dependent demand analysis under the critical pipe outage

wdsa2006 efficientpdd haestad eng lowres

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