The Effect of Pressure on Leakage in Water Distribution Systems

8/6/2019 The Effect of Pressure on Leakage in Water Distribution Systems

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THE EFFECT OF PRESSURE ON LEAKAGE IN WATER

DISTRIBUTION SYSTEMS

JE van Zyl

1

and CRI Clayton

2

1University of Johannesburg, South Africa2University of Southampton, UK

[email protected]

Abstract

The results of pressure management field studies have shown that the leakage exponent is often considerably

higher than the theoretical orifice value of 0.5. The purpose of this paper is to identify and analyse factors thatmay be responsible for the higher leakage exponents. Four factors are considered: leak hydraulics, pipematerial behaviour, soil hydraulics and water demand. It is concluded that a significant proportion ofbackground leakage can consist of transitional flow, and thus have a leakage coefficient value above 0.5(although not above 1). The most important factor is probably pipe material behaviour: laboratory test results

and a theoretical leak model is presented to show that pipe material behaviour can explain the range of leakageexponents observed in the field. The complexity of the interaction between a leaking pipe and its surroundingsoil is discussed and it is concluded that this relationship is unlikely to be linear. Finally, it is concluded that ifwater demands are present in minimum night flows, the resulting leakage exponent is probably underestimatingthe true value.

KeywordsWater losses, leakage, pressure, hydraulics, soil hydraulics, water demand

1. INTRODUCTIONThere is renewed international awareness that water distribution systems world-wide are aging and deteriorating,while the demands on these systems, and thus on our natural water resources, are ever increasing. Losses from

water distribution systems are reaching alarming levels in many towns and cities throughout the world. Waterlosses are made up of various components including physical losses (leaks), illegitimate use, unmetered use and

under-registration of water meters. Leakage makes up a large part, sometimes more than 70 % of the total waterlosses [1]. Water losses have a negative impact on the level of service provided to customers, whilst reducing theincome of water suppliers, and increasing the environmental impact of water extractions.

A considerable amount of research has been carried out to improve our understanding of leakage, and control ofwater losses. However, the goal of reducing water losses to acceptable levels remains elusive. It is now

recognised that the complexities involved in this problem are much greater than initially thought and that,although much progress has been made in understanding the various factors that affect water losses, much still

remains to be done.

One of the major factors influencing leakage is the pressure in the distribution system. In the past theconventional view was that leakage from water distribution systems is relatively insensitive to pressure, as

described by the orifice equation:

2dq C A gh= ...(1)

where q the flowrate, Cd the discharge coefficient, A the orifice area, g acceleration due to gravity and h thepressure head. To apply this equation to leaks in pipes it can be written in more general form as:

q ch= ...(2)


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where c is the leakage coefficient and the leakage exponent. A number of field studies have shown that canbe considerably larger than 0.5, and typically varies between 0.5 and 2.79 with a median of 1.15 [2]. This meansthat leakage in water distribution systems can be much more sensitive to pressure than conventionally believed.As a result, pressure management has become an established water loss control strategy and is appliedthroughout the world.

Figure 1 illustrates the huge effect of the leakage exponent on the leakage rate. If, for instance, the pressure at aleak is halved (H1/H0 = 0.5), the leakage flow rate will reduce by 29 %, 50 % and 82 % for exponents of 0.5, 1.0and 2.5 respectively. It can also be shown that the typical time taken to fill a bath through a 1 mm hole at apressure of 50 m is 2.8 hours for a leakage exponent of 0.5, and only 4 seconds if the leakage exponent is 2.5.

The purpose of this paper is to identify and analyse factors that may be responsible for the range of leakageexponents observed in the field.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

H1 / H0

q1

/q0

Exponent: 0.5 1 2.5

Fig 1. Effect of leakage exponent on the leakage rate

2. LEAK HYDRAULICSIf head losses in the surrounding soil are ignored, a leak opening in a pipe is hydraulically equivalent to anorifice on the side of a tank. The hydraulic behaviour of orifices has been researched extensively and can be

predicted with some degree of certainty. It is universally accepted that the leakage exponent of an orifice of fixeddiameter is 0.5. However, the discharge coefficient is often not constant, but is expressed as a function of theReynolds number (Re) [3]. It is thus conceivable that a certain type of leak can be modelled using a fixeddischarge coefficient, but with an exponent higher or lower than 0.5.

Another important hydraulic future comes into play in laminar flow, which is characterised by a linear

relationship between head loss and flow rate. Flow through orifices is laminar at Re below about 10 andturbulent above about 4000. Intermediate values represent the transitional zone where the leakage exponent canvary between 1 (at the laminar/transitional boundary) and 0.5 (at the transitional/turbulent boundary). Themaximum laminar and maximum transitional (or minimum turbulent) flow rates were be calculated for differenttypes of leak openings and are shown in figure 2. Round, square and rectangular leak openings were considered.Cracks are represented by a rectangular opening with a large length to width (l/b) ratio. Orifice flow and a

discharge coefficient Cd of 0.6 were assumed.

The figure shows that cracks can have much higher laminar or transitional flow rates than round or square holes.This is due to the role of their much larger wetted perimeters. The maximum possible flow rates that are fullylaminar are very small (less than 9 l/day) and it is thus unlikely that substantial losses from water distributionsystems will occur in the fully laminar zone.


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1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

10 20 30 40 50 60 70 80 90 100

Pressure Head (m)

Flowr

ate(l/s)

Round Round

Square SquareRectangular (l/b = 100) Rectangular (l/b = 100)

Rectangular (l/b = 10000) Rectangular (l/b = 10000)

Transitional flow limitLaminar flow limit

Fig 2. Maximum laminar and transitional flow rates for different types of leak openings

A distinction is often made between bursts and background leakage: bursts are large individual leaks that come

to the surface or are found through active leakage control initiatives. Background leakage comprises numeroussmall leaks that are very difficult or impossible to detect without excavating the pipe. In a well run system, muchof a networks water loss that we seek to reduce through pressure control may thus result from backgroundleakage. This view is supported by water leakage figures for England and Wales (about 25 million connected

properties) which has been estimated by OFWAT [4] in 2004 to be on average of the order of 10 m3/km of

main/day, or about 0.1 l/s/km of main. Comparing this figure with the maximum transitional flow rates aboveindicate that it is possible that much of the background leakage can occur in this range, especially in systems thatare likely to have pipes that develop long cracks. Transitional flow can thus be an important cause of a leakageexponent above 0.5 (although not above 1.0) when background leakage is a large contributor to leakage from asystem.

3. PIPE MATERIAL BEHAVIOURPipe material plays an important role in the leakage behaviour of pipes. Due to the material properties, pipes ofdifferent materials will fail in certain characteristic ways. For instance, asbestos cement pipes will typically failwith longitudinal cracks, while steel and cast iron pipes may leak through corrosion holes. Small-diameter castiron pipes typically fail in bending leading to circumferential cracks which, because of the relatively highcoefficient of thermal expansion of the pipe material, may open and close as the temperature of the water in thesystem changes. Water pressure in a pipe is taken up by stresses in the pipe wall, and thus may play an importantrole in the failure and leakage behaviour of pipes made of lower strength materials. The following effects can be

linked to an increase in the internal pressure in a pipe:

Small cracks or fractures that do not leak at low pressure and high temperature, can open up to createnew leaks at the higher pressure.

The area of an existing leak opening in a pipe can increase due to the increased stresses in the pipe wall. The frequency of pipe bursts increases [2]. Conversely, higher pressures will also make leaks easier to

find and higher pressures might thus not necessarily lead to an increase in the total number of leaks.

In an experimental study done at the University of Johannesburgs Water Research Group in 2004, Greyvenstein

[5] determined the leakage exponents for failed pipes taken from the field, and for pipes with artificially inducedleaks. The study included round holes, and longitudinal and circumferential cracks in uPVC, steel and asbestos


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cement pipes. All flows were turbulent and leaks were exposed to the atmosphere. The resulting leakageexponents varied between 0.42 and 2.4 as shown in table 1. The main findings of the study were:

The exponents found confirms that the leakage exponents found in field studies are not unrealistic. The highest leakage exponents occurred in corroded steel pipes, probably due to corrosion reducing the

support material around the hole. This is contrary to the perception [2] that plastic pipes will have

higher leakage exponents due to their lower modulus of elasticity. Round holes had leakage exponents close to the theoretical value of 0.5 and no significant difference

was observed between steel and uPVC pipes.

Besides corrosion holes, the largest exponents were found in longitudinal cracks. This is due to the factthat circumferential stresses in pipes are typically substantially higher than longitudinal stresses.

The leakage exponent for circumferential cracks in uPVC pipes could be less than 0.5, indicating thatthe leak opening is contracting with increasing pressure. This is explained by the fact that theexperimental setup did not allow substantial longitudinal stresses to develop in the pipe. It is thoughtthat the circumferential stresses caused the cracks to elongate, and at the same time reduce in area.

Table 1. Leakage exponents found in an experimental study by Greyvenstein [5]

Leakage exponent for pipe materialFailure type

uPVC Asbestos cement Mild steel

Round hole 0.52 - 0.52Longitudinal crack 1.38 1.85 0.79 1.04 -

Circumferential crack 0.41 0.53 - -

Corrosion cluster - - 0.67 2.30

Theoretical work carried out at the University of Johannesburgs Water Research Group developed the followingbasic model for the flow rate through a round hole in an elastic pipe:

++= 2

5

22

2222

2

3

2

12

0

93

22

4H

Et

DgcH

tE

gDcHg

dCQ d

... (3)

where do is the original hole diameter,D is the pipe diameter, t the pipe wall thickness,Ethe elasticity modulusand c a constant. The relationship shows that the processes involved in the expanding leak opening are morecomplex than the simple power relationship normally used to describe leakage. The equation contains the sum ofthree terms with leakage exponents of 0.5, 1.5 and 2.5 respectively, which seems to tie in well with field andexperimental observations. However, the experimental results showed that the leakage exponent is not affected

much for a round hole: the terms with exponents 1.5 and 2.5 contribute little to the leak under normal pressureconditions in a water distribution network. Work is currently under way to extend the equation for cracks, and toimprove it by incorporating variables such as Poissons ratio.

4. SOIL HYDRAULICSA simplistic application of geotechnical seepage theory would suggest, in contrast to equation (1), that if headlosses through the pipe orifice are neglected, the flow rate should be proportional to the head of the water in thepipe, h, since following Darcys Law, the flow rate (q) in the soil for a given head on the orifice water/soil

boundary will be

q =F . k . h ... (5)

whereFis the shape factor for the soil flow region, and kis the coefficient of permeability of the soil. Howeverthis equation is underpinned by a number of assumptions, and these are not generally valid for seepage around awater pipe.

Firstly, in soil seepage analysis it is generally safe to assume that the velocity component of total head is verysmall, and can be ignored. The velocity of flow through soil under a hydraulic gradient of unity varies from 10

-2

m/s for a clean coarse sand to 10-8

m/s and smaller for clays. Yet in contrast the hydraulics orifice equation

(equation (1) above) predicts very high velocities at the soil/water interface. There is clearly an incompatibilityhere, and the interface between the two systems is not properly defined by coupling the orifice equation (for flowin the absence of soil, which will in fact modify downstream behaviour, perhaps whilst also obscuring part of the


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orifice itself) with the soil seepage equation (which assumes that there is an upstream boundary with constanthead applied to it.

Secondly, the downstream boundary conditions in the ground surrounding the pipe are not generally constantregardless of flow rate. In most geotechnical seepage conditions both upstream and downstream boundaries can

reasonably be assumed to have fixed geometries and head conditions. Since water pipes are generally laid above

the ground water level the seepage flow net (and thus F in equation (4) above) varies as a function of the rate ofoutflow from the pipe and the coefficient of permeability of the soil. For any given soil permeability, increasingflow leads to progressive build-up of pore pressure in the soil around the pipe, and eventual mounding of waterabove it. For low flow rates relative to the permeability of the soil, seepage will not reach the ground surface,and leakage will go unnoticed. At higher rates of leakage water will emerge at ground surface and a burst will

be detected.

Thirdly there are limits to validity of Darcys law. A linear relationship between head and flow in soil is, asobserved by Osborne Reynolds in 1883, only valid for laminar flow. The critical value of Re (expressed in soil

mechanics as /vDR = , where v is the discharge velocity (flow per unit cross section of soil), andD is theaverage soil particle diameter) at which flow in soil changes from laminar to turbulent has been found to rangebetween about 1 and 10 (for example, see [6]) . Discharge velocity depends upon both hydraulic gradient and

permeability (which is itself a function of particle size). Under the low hydraulic gradients (h/l


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5. WATER DEMANDWater demand cannot be classified as leakage, but it is often impossible to separate legitimate waterconsumption from leakage measurements in the field. It is thus important to understand the behaviour of water

demand as a function of pressure. The effect of pressure on demand Qdem can be expressed as [8]:

demQ Ch= ... (5)

With Ca constant coefficient and the elasticity of demand to pressure. There is a clear resemblance betweenequations for leakage (equation 2) and demand elasticity (equation 5). The elasticity includes the effects ofhuman behaviour, such as reacting to an increased pressure by opening taps less to obtain the same flow rate. Ina study of water consumption patterns at a student village on the campus of the University of Johannesburg,Bartlett [9] found the indoor demand elasticity for pressure to be approximately 0.2. Outdoor water consumption

such as garden irrigation is typically time-based rather than volume-based, meaning that a higher exponent canbe expected for outdoor use, although this exponent is unlikely to exceed 0.5.

In large systems it becomes likely that even minimum measured night flows will include some legitimateconsumption. Since the combined leakage exponent for outdoor and indoor consumption is likely to be lessthan 0.5, it may be concluded that measured leakage exponents in systems with demand are likely to

underestimate the true leakage exponent of the system, provided that the level of demand in the measured nightflows do not differ significantly.

6. CONCLUSIONSThe leakage exponent determined from field studies differ significantly from the theoretical orifice exponent of0.5. The purpose of this paper was to identify and analyse factors that may be responsible for the range ofleakage exponents observed in the field. Leak hydraulics, pipe material behaviour, soil hydraulics and waterdemand were considered as possible causative factors. It is concluded that a significant proportion of backgroundleakage can consist of transitional flow, and thus have a leakage coefficient value above 0.5 (although not above

1). Pipe material behaviour provide the most likely explanation for the observed range of leakage exponents.Both experimental and theoretical investigations indicate that material behaviour is a likely explanation for theobserved leakage exponents. It was concluded that the interaction between a leaking pipe and its surroundingsoil is complex, and unlikely to be linear, as a result of interaction of soil particles with the orifice, turbulent flowin the soil, the changing geometry of the unconfined flow regime, hydraulic fracturing and piping. Finally, ifwater demands are present in minimum night flows, the resulting leakage exponent is probably underestimating

the true value.

References

[1] WHO - World Health Organisation, LeakageManagement and Control - A Best Practice Manual, WHO,Geneva, 2001[2] Farley, M., and Trow, S. (2003) Losses in Water Distribution Networks, IWA Publishing, London

[3] Idelchik, I., E., Handbook of Hydraulic Resistance, 3rd Edition, Begell House, New York[4] OFWAT - Office of Water Services (2004) Security of supply, leakage and the efficient use of water 2003-

2004 Report, OFWAT, Birmingham, December 2004, 86pp.[5] Greyvenstein, B.,An Experimental Investigation into the Pressure-Leakage Relationship of Some Failed

Water Pipes in Johannesburg, B.Eng. Final Year Project Report, Department of Civil and UrbanEngineering, Rand Afrikaans University (now University of Johannesburg), South Africa, 2004

[6] Harr, M.E. (1962) Groundwater and seepage, McGraw Hill, New York, 315pp.[7] Bjerrum, L.J., Nash, J.K.T.L., Kennard, R.M. and Gibson, R.E. (1072) Hydraulic fracturing in field

permeability testing Geotechnique, vol. 22, no.2, pp.319-332.[8] Van Zyl, J.E., Haarhoff, J., Husselmann, M.L. (2003) Potential Application of End-use Demand Modelling

in South Africa,Journal of the South African Institute of Civil Engineering, 45 (2).

[9]

Bartlett, L. (2004) Pressure Dependant Demands in Student Town Phase 3, B.Eng. Final Year ProjectReport, Department of Civil and Urban Engineering, Rand Afrikaans University (now University ofJohannesburg), South Africa, 2004

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The Effect of Pressure on Leakage in Water Distribution Systems