Managing Leakage by District Metered Areas

Managing Leakage by Managing Leakage by

District Metered District Metered AreasAreas

Part IPart ILeakage TheoryLeakage Theory

IntroductionIntroduction

Main factors that influence leakage: Main factors that influence leakage: Infrastructure condition Infrastructure condition Pressure Pressure Service connections - number, ownership and Service connections - number, ownership and location of customer meters location of customer meters Length of mains Length of mains Annual number of new leaks (reported and Annual number of new leaks (reported and unreported) on mains unreported) on mains Annual number of new leaks (reported and Annual number of new leaks (reported and unreported) on service connections unreported) on service connections Average run-times of reported and unreported Average run-times of reported and unreported leaks leaks


The frequency at which new bursts and leaks The frequency at which new bursts and leaks occur depends upon the overall condition of the occur depends upon the overall condition of the infrastructure and how well the pressures in the infrastructure and how well the pressures in the distribution system are managed. distribution system are managed.

Dependent upon the specific ground type there Dependent upon the specific ground type there will always be a proportion of leaks and bursts will always be a proportion of leaks and bursts that do not appear on the surface i.e. non-visible that do not appear on the surface i.e. non-visible or unreported leaks and these need to be or unreported leaks and these need to be detected. detected.

Components of Real Losses or Components of Real Losses or LeakageLeakage

Reported leaks and breaks Reported leaks and breaks Typically high flow rates, short run-time notified to the water Typically high flow rates, short run-time notified to the water

utility by customers etc utility by customers etc Are usually: phoned in by the public · visible · found followinAre usually: phoned in by the public · visible · found followin

g complaints of low pressure or no supply · observed by meg complaints of low pressure or no supply · observed by meter readers and maintenance teamster readers and maintenance teams

Unreported leaks and breaks Unreported leaks and breaks Typically moderate flow rates, long run-time located by activTypically moderate flow rates, long run-time located by activ

e leakage control e leakage control Are usually: non-visible · found by active leakage controlAre usually: non-visible · found by active leakage control

Background leakage (mostly at joints and fittings) Background leakage (mostly at joints and fittings) flow rates too small to be detected if hidden generally < 25flow rates too small to be detected if hidden generally < 25

0 litres/hour, (1 gpm), but run continuously 0 litres/hour, (1 gpm), but run continuously

Volumes of Water Lost from Leaks Volumes of Water Lost from Leaks and Bursts and Bursts

Where do Most Real Losses Where do Most Real Losses Occur? Occur?

from background leakage from background leakage

from long-running unreported leaks and bursts from long-running unreported leaks and bursts

from long-running reported leaks which the water from long-running reported leaks which the water utility does not bother to repair utility does not bother to repair

Part IIPart IILeakage Monitoring:Leakage Monitoring:

DMA ConceptDMA Concept


A District Meter Area A District Meter Area ((DMADMA)) is an area of between is an area of between 500 and 3000 connections into which water can 500 and 3000 connections into which water can be measured and analyzed to determine the level be measured and analyzed to determine the level of leakage.of leakage.

This is called This is called leakage monitoringleakage monitoring, and should be , and should be introduced in order for the activities of leak introduced in order for the activities of leak localizing and leak location to be truly effective.localizing and leak location to be truly effective.

The technique requires the installation of The technique requires the installation of flow flow metersmeters at strategic points throughout the at strategic points throughout the distribution system, each recording flows to a distribution system, each recording flows to a discrete district that has a defined and discrete district that has a defined and permanent boundary - the DMA. permanent boundary - the DMA.

Division of Distribution Network into DMA Division of Distribution Network into DMA

Estimating leakageEstimating leakage

Estimation of leakage when the flow into the DMA Estimation of leakage when the flow into the DMA is at its minimum.is at its minimum. at night when customer demand is at its at night when customer demand is at its

minimum and therefore the leakage component minimum and therefore the leakage component is at its largest percentage of the flow. is at its largest percentage of the flow.


The analysis of leakage is based on the The analysis of leakage is based on the minimum night minimum night flowflow, which can be recorded and analyzed continuously , which can be recorded and analyzed continuously night after night with the use of data loggers and night after night with the use of data loggers and appropriate software. appropriate software.

One of the techniques is when analysis is concentrated on One of the techniques is when analysis is concentrated on night use allowances and 15 minutes flow sampling night use allowances and 15 minutes flow sampling intervals using standard meters and loggers.intervals using standard meters and loggers.

It is recommended that reported leakage is based on a It is recommended that reported leakage is based on a rolling 7 day 20 percentile using the minimum rolling hour rolling 7 day 20 percentile using the minimum rolling hour each night. The method will give a leakage estimate for each night. The method will give a leakage estimate for each day.each day.

Monthly and annual estimates should be based on the Monthly and annual estimates should be based on the average of available data for the relevant period.average of available data for the relevant period.


Based on this analysis, summary reports of estimated leakage from bursts in individual DMAs can be developed to provide the leBased on this analysis, summary reports of estimated leakage from bursts in individual DMAs can be developed to provide the leakage practitioner with a schedule of leakage that can be reduced.akage practitioner with a schedule of leakage that can be reduced.This reduction can be represented as a volume of water, a potential number of bursts that can be found, an estimate of the cost This reduction can be represented as a volume of water, a potential number of bursts that can be found, an estimate of the cost of leakage that is being lost, or a ranking system developed to suit local conditions. When fully developed this analysis will enable of leakage that is being lost, or a ranking system developed to suit local conditions. When fully developed this analysis will enable a leakage practitioner to monitor a large number of DMAs effectively and focus work in key DMAs, which will generate most benefia leakage practitioner to monitor a large number of DMAs effectively and focus work in key DMAs, which will generate most benefit from leak location.t from leak location.The level of leakage can be further confirmed by a 'top down' assessment of leakage. This analysis requires an assessment of cuThe level of leakage can be further confirmed by a 'top down' assessment of leakage. This analysis requires an assessment of customer use, which is subtracted from the total flow into the area to estimate leakage. In most instances this leakage volume, mestomer use, which is subtracted from the total flow into the area to estimate leakage. In most instances this leakage volume, measured over a period of 6 to 12 months, will be compared with the aggregate of leakage from DMAs in the same area. asured over a period of 6 to 12 months, will be compared with the aggregate of leakage from DMAs in the same area.

Water DemandWater Demand

One of the most important aspects of modeling leakage in watOne of the most important aspects of modeling leakage in water systems is the modeling of the demand for water from the er systems is the modeling of the demand for water from the water supply system.water supply system.The demand for water in a given area can be divided into the fThe demand for water in a given area can be divided into the following ollowing

domestic consumption domestic consumption metered consumption metered consumption unmetered consumption unmetered consumption losses (including leakage) losses (including leakage) exceptional demand (for example transfers)exceptional demand (for example transfers)

An important fact in demand modeling is that the pattern of deAn important fact in demand modeling is that the pattern of demand for a particular type of customer remains fairly constant. mand for a particular type of customer remains fairly constant.

Demand ProfileDemand Profile

Daily Variations Daily Variations

Working vs.Working vs.

Weekend DaysWeekend Days

Demand ProfileDemand ProfileSeasonal Variations:Seasonal Variations:

the range of maximum and minimum temperatures the range of maximum and minimum temperatures humidity humidity holiday season holiday season local customslocal customs

Weather Conditions Weather Conditions The pattern for dry and hot weather features two The pattern for dry and hot weather features two

prominent peaks, morning and evening. For rainy prominent peaks, morning and evening. For rainy days the pattern is significantly different. The days the pattern is significantly different. The second peak has almost disappeared. If it rains, second peak has almost disappeared. If it rains, there is no need to water the garden. there is no need to water the garden.

Leakage analysis records Leakage analysis records

Records required are those which relate to the calculation Records required are those which relate to the calculation of net night flow and leakage from total night flow in each of net night flow and leakage from total night flow in each DMA, using the basic formula: DMA, using the basic formula:

Leakage (total night flow losses) = Leakage (total night flow losses) = min. night flow—min. night flow—customer usecustomer use

number of properties number of properties

or or min. night flow—customer usemin. night flow—customer use

length of mainlength of main


Records required areRecords required are: : night flows at each meter; night flows at each meter; non-metered household count;— occupancy rate; non-metered household count;— occupancy rate; numbers of metered users in each categorynumbers of metered users in each category large industrial users; large industrial users; allowances for night use; allowances for night use; net night flow; net night flow; average zone night pressure; average zone night pressure; pressure profile at mid-zone; pressure profile at mid-zone; hour to day factor.hour to day factor.


Night flows Night flows should be recorded at selected intervals over a selected should be recorded at selected intervals over a selected

period, adding and/or subtracting flows from multiple DMA period, adding and/or subtracting flows from multiple DMA metersmeters

Non metered household count Non metered household count should be entered in the file for each DMA, and updated should be entered in the file for each DMA, and updated

regularly. regularly.

Metered users Metered users Record the number of metered customers in each category, Record the number of metered customers in each category,

preferably using Standard Industrial Classification (SIC) codespreferably using Standard Industrial Classification (SIC) codes Record the total estimated night use of each category, based Record the total estimated night use of each category, based

on customer demand studies. on customer demand studies. Include non-metered commercial properties in the domestic Include non-metered commercial properties in the domestic

property count, unless they are significant night users. property count, unless they are significant night users.


Customer night use Customer night use relate to each of the customer categories and their night use. Night relate to each of the customer categories and their night use. Night

use is an important record as it is subtracted from night flow use is an important record as it is subtracted from night flow delivered to derive leakage on non-metered household service pipes, delivered to derive leakage on non-metered household service pipes, and their plumbing losses, in the DMA. and their plumbing losses, in the DMA.

Large metered customers Large metered customers Customers who use significant amounts of water at night should have Customers who use significant amounts of water at night should have

their night flows recorded simultaneously with DMA monitoring. their night flows recorded simultaneously with DMA monitoring.

Other metered customers Other metered customers Consider a study of each category to provide a better estimate of Consider a study of each category to provide a better estimate of

night consumption. night consumption.

Operational use Operational use This includes water abstracted for night mains flushing and fire This includes water abstracted for night mains flushing and fire

fighting, which, although comparatively small, may influence fighting, which, although comparatively small, may influence minimum night flow readings on a particular night. minimum night flow readings on a particular night.

Part IIIPart IIIARMA ModelARMA Model

IntroductonIntroducton

In statistics, In statistics, autoregressive moving average (ARMA) modelsautoregressive moving average (ARMA) models, so, sometimes called Box-Jenkins models after the iterative Box-Jenkimetimes called Box-Jenkins models after the iterative Box-Jenkins methodology usually used to estimate them, are typically appns methodology usually used to estimate them, are typically applied to time series data.lied to time series data.Given a time series of data XGiven a time series of data Xtt, the ARMA model is a tool for und, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series.erstanding and, perhaps, predicting future values in this series.The model consists of two parts, an The model consists of two parts, an autoregressive (AR)autoregressive (AR) part an part and a d a moving average (MA)moving average (MA) part. part.ARMA(p,q): p is the order of the autoregressive part and q is the ARMA(p,q): p is the order of the autoregressive part and q is the order of the moving average part.order of the moving average part.

Autoregressive ModelAutoregressive Model

AR(p) refers to the AR(p) refers to the autoregressive modelautoregressive model of order p: of order p:

φφii… … φφpp are the parameters of the model, c is a constant and are the parameters of the model, c is a constant and εε tt is is an error terman error term

An AR(1)-process is given by: An AR(1)-process is given by:

where where εε tt is a white noise process with zero mean and variance is a white noise process with zero mean and variance σσ22

The process is The process is covariance-stationarycovariance-stationary if | if |φφ|<1|<1 Stationary process: stochastic process whose probability distribution is the same for all timStationary process: stochastic process whose probability distribution is the same for all tim

es or positions es or positions

AR(1) ProcessAR(1) Process

AR(1) process is given byAR(1) process is given by

Assuming covariance-stationary:Assuming covariance-stationary:

where where μμis the mean.is the mean.The variance isThe variance is

The autocovariance (covariance of the signal against a time-shifThe autocovariance (covariance of the signal against a time-shifted version of itself) isted version of itself) is

Calculation of AR ParametersCalculation of AR Parameters

AR(p) model is given byAR(p) model is given by

It is based on parameters It is based on parameters φφ where i = 1, ..., p. Those parameters may be calculated using least squares regression where i = 1, ..., p. Those parameters may be calculated using least squares regression or the Yule-Walker equations: or the Yule-Walker equations:

where m = 0, ... , p, yielding p + 1 equations. γwhere m = 0, ... , p, yielding p + 1 equations. γmm is the autocorrelati is the autocorrelation function of X, on function of X, σσεε is the standard deviation of the input noise procis the standard deviation of the input noise process, and δess, and δmm is the Kronecker delta function: is the Kronecker delta function:

Calculation of AR ParametersCalculation of AR Parameters

Because the last part of the equation is non-zero only if m = 0, the equation is usually solved by Because the last part of the equation is non-zero only if m = 0, the equation is usually solved by representing it as a matrix for m > 0, thus getting equation representing it as a matrix for m > 0, thus getting equation

solving all solving all φφ. For m = 0 have . For m = 0 have

which allows us to solve which allows us to solve σσεε22..

DerivationDerivation

E[XE[XttXXt m−t m− ] = γ] = γmm by definition of the autocorrelation function. by definition of the autocorrelation function.

The values of the noise function are independent of each other, aThe values of the noise function are independent of each other, and Xnd Xt m−t m− is independent of ε is independent of εtt where m > 0. For m > 0, E[ε where m > 0. For m > 0, E[εttXXt m−t m− ] = ] = 0. For m = 0, 0. For m = 0,

AR(p) model is given byAR(p) model is given by

Multiplying both sides by XMultiplying both sides by Xt-mt-m and taking expected value: and taking expected value:

DerivationDerivation

which yields the Yule-Walker equations for m≥0: which yields the Yule-Walker equations for m≥0:

Now we have, for m ≥ 0 Now we have, for m ≥ 0

Multiplying both sides by XMultiplying both sides by Xt-mt-m and taking expected value: and taking expected value:

For m<0For m<0

Moving Average ModelMoving Average Model

MA(q) refers to the MA(q) refers to the moving average modelmoving average model of order q: of order q:

θθii… … θθqq are the parameters of the model, are the parameters of the model, εε tt, , εε t-1t-1 are error terms are error terms

Autoregressive Moving Autoregressive Moving Average ModelAverage Model

ARMA(p,q) refers to the ARMA(p,q) refers to the autoregressive moving average modelautoregressive moving average model w with ith pp autoregressive terms and autoregressive terms and qq moving average terms. This m moving average terms. This model contains the AR(p) and MA(q) models:odel contains the AR(p) and MA(q) models:

Managing Leakage by District Metered Areas

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