1. Managing Leakage by District Metered Areas

2. Part I Leakage Theory

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

4. Introduction The frequency at which new bursts and leaks occur depends upon the overall condition of the infrastructure and how well the pressures in the distribution system are managed. Dependent upon the specific ground type there will always be a proportion of leaks and bursts that do not appear on the surface i.e. non-visible or unreported leaks and these need to be detected.

5. Components of Real Losses or Leakage Reported leaks and breaks Typically high flow rates, short run-time notified to the water utility by customers etc Typically high flow rates, short run-time notified to the water utility by customers etc Are usually: phoned in by the public · visible · found following complaints of low pressure or no supply · observed by meter readers and maintenance teams Are usually: phoned in by the public · visible · found following complaints of low pressure or no supply · observed by meter readers and maintenance teams Unreported leaks and breaks Typically moderate flow rates, long run-time located by active leakage control Typically moderate flow rates, long run-time located by active leakage control Are usually: non-visible · found by active leakage control Are usually: non-visible · found by active leakage control Background leakage (mostly at joints and fittings) flow rates too small to be detected if hidden generally < 250 litres/hour, (1 gpm), but run continuously flow rates too small to be detected if hidden generally < 250 litres/hour, (1 gpm), but run continuously

6. Volumes of Water Lost from Leaks and Bursts

8. Where do Most Real Losses Occur? from background leakage from long-running unreported leaks and bursts from long-running reported leaks which the water utility does not bother to repair

9. Part II Leakage Monitoring: DMA Concept

10. Introduction A District Meter Area (DMA) is an area of between 500 and 3000 connections into which water can be measured and analyzed to determine the level of leakage. This is called leakage monitoring, and should be introduced in order for the activities of leak localizing and leak location to be truly effective. The technique requires the installation of flow meters at strategic points throughout the distribution system, each recording flows to a discrete district that has a defined and permanent boundary - the DMA.

11. Division of Distribution Network into DMA

12. Estimating leakage Estimation of leakage when the flow into the DMA is at its minimum. at night when customer demand is at its minimum and therefore the leakage component is at its largest percentage of the flow. at night when customer demand is at its minimum and therefore the leakage component is at its largest percentage of the flow.

13. Estimating leakage The analysis of leakage is based on the minimum night flow, which can be recorded and analyzed continuously night after night with the use of data loggers and appropriate software. One of the techniques is when analysis is concentrated on night use allowances and 15 minutes flow sampling intervals using standard meters and loggers. It is recommended that reported leakage is based on a rolling 7 day 20 percentile using the minimum rolling hour each night. The method will give a leakage estimate for each day. Monthly and annual estimates should be based on the average of available data for the relevant period.

14. Estimating leakage Based 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. 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 a leakage practitioner to monitor a large number of DMAs effectively and focus work in key DMAs, which will generate most benefit from leak location. The 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, measured over a period of 6 to 12 months, will be compared with the aggregate of leakage from DMAs in the same area.

15. Water Demand One of the most important aspects of modeling leakage in water systems is the modeling of the demand for water from the water supply system. The demand for water in a given area can be divided into the following 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 demand for a particular type of customer remains fairly constant.

16. Demand Profile Daily Variations Working vs. Weekend Days Weekend Days

17. Demand Profile Seasonal Variations: the range of maximum and minimum temperatures the range of maximum and minimum temperatures humidity humidity holiday season holiday season local customs local customs Weather Conditions The pattern for dry and hot weather features two prominent peaks, morning and evening. For rainy days the pattern is significantly different. The second peak has almost disappeared. If it rains, there is no need to water the garden. The pattern for dry and hot weather features two prominent peaks, morning and evening. For rainy days the pattern is significantly different. The second peak has almost disappeared. If it rains, there is no need to water the garden.

18. Leakage analysis records Records required are those which relate to the calculation of net night flow and leakage from total night flow in each DMA, using the basic formula: Leakage (total night flow losses) = min. night flow—customer use Leakage (total night flow losses) = min. night flow—customer use number of properties number of properties or min. night flow—customer use length of main length of main

19. Leakage analysis records Records 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 category numbers 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.

20. Leakage analysis records Night flows should be recorded at selected intervals over a selected period, adding and/or subtracting flows from multiple DMA meters should be recorded at selected intervals over a selected period, adding and/or subtracting flows from multiple DMA meters Non metered household count should be entered in the file for each DMA, and updated regularly. should be entered in the file for each DMA, and updated regularly. Metered users Record the number of metered customers in each category, preferably using Standard Industrial Classification (SIC) codes Record the number of metered customers in each category, preferably using Standard Industrial Classification (SIC) codes Record the total estimated night use of each category, based on customer demand studies. Record the total estimated night use of each category, based on customer demand studies. Include non-metered commercial properties in the domestic property count, unless they are significant night users. Include non-metered commercial properties in the domestic property count, unless they are significant night users.

21. Leakage analysis records Customer night use relate to each of the customer categories and their night use. Night use is an important record as it is subtracted from night flow delivered to derive leakage on non-metered household service pipes, and their plumbing losses, in the DMA. relate to each of the customer categories and their night use. Night use is an important record as it is subtracted from night flow delivered to derive leakage on non-metered household service pipes, and their plumbing losses, in the DMA. Large metered customers Customers who use significant amounts of water at night should have their night flows recorded simultaneously with DMA monitoring. Customers who use significant amounts of water at night should have their night flows recorded simultaneously with DMA monitoring. Other metered customers Consider a study of each category to provide a better estimate of night consumption. Consider a study of each category to provide a better estimate of night consumption. Operational use This includes water abstracted for night mains flushing and fire fighting, which, although comparatively small, may influence minimum night flow readings on a particular night. This includes water abstracted for night mains flushing and fire fighting, which, although comparatively small, may influence minimum night flow readings on a particular night.

22. Part III ARMA Model

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

24. Autoregressive Model AR(p) refers to the autoregressive model of order p: φ i … φ p are the parameters of the model, c is a constant and ε t is an error term An AR(1)-process is given by: where ε t is a white noise process with zero mean and variance σ 2 The process is covariance-stationary if |φ|<1 Stationary process: stochastic process whose probability distribution is the same for all times or positions Stationary process: stochastic process whose probability distribution is the same for all times or positions

25. AR(1) Process AR(1) process is given by Assuming covariance-stationary: where μis the mean. The variance is The autocovariance (covariance of the signal against a time- shifted version of itself) is

26. Calculation of AR Parameters AR(p) model is given by It is based on parameters φ where i = 1,..., p. Those parameters may be calculated using least squares regression or the Yule-Walker equations: where m = 0,..., p, yielding p + 1 equations. γ m is the autocorrelation function of X, σ ε is the standard deviation of the input noise process, and δ m is the Kronecker delta function:

27. Calculation of AR Parameters 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 solving all φ. For m = 0 have which allows us to solve σ ε 2.

28. Derivation E[X t X t−m ] = γ m by definition of the autocorrelation function. The values of the noise function are independent of each other, and X t−m is independent of ε t where m > 0. For m > 0, E[ε t X t − m ] = 0. For m = 0, AR(p) model is given by Multiplying both sides by X t-m and taking expected value:

29. Derivation which yields the Yule-Walker equations for m≥0: Now we have, for m ≥ 0 Multiplying both sides by X t-m and taking expected value: For m<0

30. Moving Average Model MA(q) refers to the moving average model of order q: θ i … θ q are the parameters of the model, ε t, ε t-1 are error terms

31. Autoregressive Moving Average Model ARMA(p,q) refers to the autoregressive moving average model with p autoregressive terms and q moving average terms. This model contains the AR(p) and MA(q) models: