## Water Balance Components and Performance Indicators Uncertainty Reduction - Požarevac Waterworks Case Study

Branislav Babić^{1}

^{1} University of Belgrade – Faculty of Civil Engineering, Bul. kralja Aleksandra 73, 11000 Belgrade, Serbia, Email:
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### Abstract

All estimates of water balance components and performance indicators include errors and uncertainties. The accuracy and reliability of these calculations depends on the accuracy and reliability of the measured data. The uncertainty of the input data is propagated to the calculated values of the system performance indicators. The quantification of the input data uncertainty and its propagation allows the water utility to determine the priorities on which data quality control activities should be focused in order to increase the reliability of the water balance components and performance indicator estimates. This paper presents the application of the ISO methodology for estimation of input data uncertainty propagation to the performance indicator of a water distribution system. A methodology for reduction of input data uncertainty, consisting of a total of seven activities implemented in sequence, is developed and tested in the Požarevac water distribution system. The implemented methodology resulted in significant reduction of uncertainty in the performance indicators and water balance components, but actual values of performance indicators did not improve.

**Keywords:** water supply, water balance, distribution systems, performance indicators, uncertainty.

Introduction

The ultimate goal of each Performance Indicator (PI) system is to provide information and data that can be used for decision-making purposes. The PI system is not only used to obtain PI values, but also to identify all the accompanying elements required in facilitating the decision-making process (data quality, elements that explain the value of indicators, elements that provide information about company characteristics). Thus, the PI system includes a set of performance and data indicators representing the real state of the water supply system (Alegre et al., 2006).

All water balance components and performance indicators in water supply services include calculations which use various input data. These input data cannot be regarded as accurate, but only as a"best estimate" to a greater or lesser extent, so the uncertainty of calculated values depends on the uncertainty of the input (measured) data (Babić et al., 2014). The quantification of uncertainties of calculated water balance components and performance indicators is of great importance because it allows the water utility to define the priorities in which data quality control activities should be focused in order to improve the reliability of the water balance components and PI estimates.

Analysis of errors and uncertainties involves the study and assessment of uncertainty, since no measurement, no matter how carefully performed, that is without uncertainty. There are different methods for the analysis of uncertainty, and each has its positive and negative aspects. However, there has been no coherent and widely accepted methodology for reduction of the water balance components and performance indicators uncertainty in water supply services developed thus far.

Bargiel and Hainsworth (1989) used the Monte Carlo simulation method to evaluate the uncertainty of pressure and flow in water distribution systems (WDS). Sattary et al. (2002) used ISO guidelines for estimating uncertainty of water balance components. Herrero et al. (2003) also used the ISO methodology for the propagation of uncertainty to estimate the impact of the uncertainty of the input variables to PIs (ISO/IEC 2008). The ISO methodology, which includes the law of propagation of indeterminacy, is now accepted as a standard method for estimating uncertainty in measurements.

Uncertainty is, in general, caused by a number of combinations of factors with randomly distributed effects. In this case, the difference between the correct and the measured value is variable with the normal distribution. Uncertainty can also be expressed through the corresponding standard deviation (σ) (Babić et al., 2014).

The combined uncertainty of measurement is obtained by combining individual standard uncertainty of the input values. The most commonly used is the First Order Second Moment (FOSM) method of propagation of uncertainty in which the uncertainty of the model parameter is transmitted through the model using the approximation of the Taylor model around the mean value of each input parameter. The uncertainty of the output variable can be obtained from the equation (1):

(1)

where* f _{k}(x_{1},...,x_{n})* is the result of the model,

*var[f*denotes the variation of the output variable,

_{k}(x_{1},...,x_{n}]*n*is the number of input variables,

*var[x*is the variant of the input

_{i}]*x*and

_{i}*cov[x*represents a covariant between the inputs

_{i},x_{j}]*x*and

_{i}*x*(cov[

_{j}*x*] = σ

_{i},x_{j}*x*).

_{i}x_{j}The derivative *∂f _{k} (x_{1},..., x_{n})/∂x_{j}* is the sensitivity of the results of the model with respect to the change in the input value

*∂x*.

_{j}The first member of the equation (1) represents the contribution to the uncertainty of the results from the uncertainty of each input variable acting independently. The second member indicates the contribution of the uncertainty of the results from the connection of the pairs of input variables. However, as the input parameters in the water balance are not measured simultaneously, and have a variety of assessment procedures, they are not correlated and the covariance is zero.

The total uncertainty of the arbitrary function f is possible to determine by using corresponding computational operations. However, for some more complex calculations, the probability of uncertainty cannot be analytically determined, so some other methods need to be applied. One of the most commonly used methods for this type of calculation is the Monte Carlo method.

This paper presents the analysis of water balance components and PIs, as well as the propagation of uncertainty to the results, in the case of the Požarevac Water Distribution System (WDS). The analysis included the following PIs (Alegre et al., 2006):

- Inefficient use of water resources,
*WR1*(%), which represents the percentage of the water that enters the system and is lost by leakage and overflows up to the point of customer metering; - Water losses per connection,
*Op23*(m^{3}/conn.year), which represents the annual volume lost per service connection in the WDS; - Water losses per mains length,
*Op24*(L/km.day), which represents the annual volume lost per mains length in the WDS; - Apparent losses per system input volume,
*Op26*(%), which represents the percentage of the water entering the system that corresponds to apparent losses in the WDS; - Real losses per connection,
*Op27*(L/conn./day), when system is pressurized, which represents real losses expressed in terms of average daily volume lost per connection in the WDS; - Real losses per mains length,
*Op28*(L/km.day), when system is pressurized, which represents real losses expressed in terms of the average daily volume lost per mains length in the WDS; - Non-revenue water
*Fi47*(%), which represents the percentage of the system input volume that corresponds to the valuation of non-revenue water components.

Methodology for Reduction of PI Uncertainty

PI Uncertainty Calculation

Uncertainty of PIs of water supply services can be determined by applying ISO methodologies for determining uncertainty propagation. According to this methodology, the equations for calculating uncertainty of selected PIs are given below:

Uncertainty of the *WR1* indicator is:

(2)

Uncertainty of the *Op23* indicator is:

(3)

Uncertainty of the* Op24* indicator is:

(4)

Uncertainty of the *Op26* indicator is:

(5)

Uncertainty of the* Op27* indicator is:

(6)

Uncertainty of the* Op28* indicator is:

(7)

Uncertainty of the *Fi47 *indicator is:

(8)

where: *V _{inflow}* - water input into the WDS (m

^{3}) and Δ

*V*- 95% confidence limit (CL), CARL – current annual real losses expressed in units volume per time (Thorton et al. 2008) and Δ

_{inflow}*CARL*- 95% CL,

*L*– mains length (km) and Δ

_{m}*L*- 95% CL,

_{m}*N*– number of service connections (-) i Δ

_{conn}*N*- 95% CL,

_{conn}*V*– apparent losses (m

_{AL}^{3}) i Δ

*V*- 95% CL,

_{AL}*WL*– total water lesses (m

^{3}) i Δ

*WL*- 95% CL,

*NRW*– non revenue water and Δ

*NRW*- 95% CL.

Methodology for Reduction of Uncertainty of Water Balance Components and PI

The methodology includes the following activities, implemented in a sequence, one after another (Babić et al., 2014):

Project Start – Activity 1: Analyses of the available data on the WDS, including the data on pipes, facilities, consumers, water consumption, existing databases, measurements, etc.. Based on existing data, the water balance components and PIs, as well as the uncertainties of the input data and their propagation, are calculated.

Activity 2: Installation of high reliability flow meters at all WDS water sources, if these do not already exist. If they exist, they should either be calibrated or their replacement with meters of greater accuracy should be considered. Since the input volume of the supplied water has the highest value of all the components of the water balance, it is of utmost importance to ensure high accuracy of the main flow meter and low uncertainty of measured input volume.

Activity 3: Designing a GIS and database of the WDS facilities, water consumers, including the water billing software.

Activity 4: Recording, locating and entering all consumers into the water consumption database and the GIS, including consumers whose consumption is metered as well as consumers whose water consumption is billed on a lump sum basis. In almost all WDSs determining the volume of authorized billed water consumption usually represents the second largest source of errors or uncertainty, immediately following system input volume measurements.

Activity 5: Water meter reading over a period of at least one year and entry of metered water consumption data into the database and the consumption analysis of all consumer categories. At this stage, it is recommended to conduct an assessment of the accuracy of consumer water meters within different categories, which can be performed on a statistical sample of water meters.

Activity 6: Detection and identification of all WDS elements (pipe diameter, length and type of pipe material, length of service connection pipes) and the entering of such data into the GIS.

Activity 7: The establishment of a mathematical model using a software package for WDS modelling, which preferably has a connection with the consumer database and the GIS. Defining flow and pressure measuring spots within the WDS for the purpose of model calibration, establishing measuring spots, performing measurements and mathematical model calibration.

Throughout the implementation of activities 1 - 7, propagation of uncertainty of input data is also performed, and the uncertainty of the water balance components and PIs is recalculated.

Description of the Požarevac WDS

The Methodology described in the previous section was applied in the Požarevac WDS, Serbia. The Požarevac WDS supplies water to about 50,000 residents, public institutions and commercial consumers. By the end of 2008 a comprehensive project for the reconstruction and improvement of the efficiency of the Požarevac WDS was initiated. The project consisted of the reconstruction of existing and the construction of new pipelines and water tanks, while a separate component of the project was the implementation of a program to increase the efficiency of the water supply services, including the reduction of water losses. The entire project was implemented in the 2008-2013 period (Ehting, 2013).

Based on the data available to the Public Utility Company (PUC) "Požarevac Waterworks and Sewerage", the total water input volume to the WDS at the beginning of the project, in 2008, was estimated to be around 6.54 million m^{3}/year (an average of 207.4 l/s). The total billed water consumption was about 3.93 million m^{3}/year (124.6 l/s), and households (residential houses and residential buildings) accounted for 64.3% of the total consumption (residential houses 46.9% and residential buildings 17.4%). The average number of monthly water bills (invoices) in the same year was about 12,400, of which 10% is for industry and 90% for households (45% residential houses and 45% residential buildings). Precise data on illegal consumers was not available, and only rough estimates exited.

At the beginning of the project, data on the total length of the water supply pipelines was very unreliable: the Master Plan of Požarevac, completed just before the start of the project, estimated about 100 km of distribution pipelines, while the internal data of the PUC pointed to a slightly higher estimated pipeline length, from 130 to 150 km. According to the available information at that time, the most common pipe materials used were asbestos cement (53.5%) and plastics (35.0%).

Results and Discussion

Based on the data available at the beginning of the project (year 2008), components of the water balance and values of PIS were calculated, as well as their uncertainty. Figure 1 shows calculated water balance components in accordance with IWA guidelines (Alegre at al., 2006; AWWA, 2009; Thornton et al. 2009.; Babić et al., 2014), with estimated uncertainties for a 95% confidence limit.

Figure 1: Estimated values of water balance components (m^{3}/yr) and their uncertainty at the beginning of the project (data for 2008).

After performing activities 2, 3, 4, 5, 6 and 7, the water balance components and their uncertainties were recalculated in 2013 and shown in Figure 2.

Figure 2: Estimated values of water balance components (m^{3}/yr) and their uncertainty after performing activities 2, 3, 4, 5, 6 and 7 (year 2013).

As a result of all the project activities, it was detected that the total length of the water supply network is about 175 km. The pipes are plastic (PE100, PE80 and PVC) measuring a total length of 99 km (56.4%) and asbestos cement measuring a total length of 55.5 km (31.7%). Pipes with a diameter of less than 100 mm were 112.8 km in total length (64.5%).

It is also significant that the average number of monthly bills increased to about 17,730 water bills, of which 10% is for industry and 90% for households (54% residential houses and 36% residential buildings).

From the above results, it can be seen that at the beginning of the project, the uncertainty of the input data was extremely high, which contributed to the uncertainty of the estimated values of the water balance components and the ILI (Infrastructure Leakage Index). Measuring input volumes (inflow) represented the biggest source of uncertainty. Installation of a new flow meter with a higher accuracy, significantly decreased uncertainty for water balance components (Babić et al., 2014).

Comparing the results for water balance components from figures 1 and 2 it can be concluded that uncertainty for all components was significantly reduced, except for unbilled authorised consumption and apparent losses. However, from figure 2 it can be concluded that, following the implementation of activities 2 through 7, the actual performance of the water supply has deteriorated: system input volume is higher, authorised consumption and revenue water is lower, water losses and non revenue water (NRW) are higher than initially estimated. It should be noted that in the 2008-2013 period there were several external factors that could influence water consumption, the most important were the gradual increase of water rates during that time period in addition to an economic crisis that led to the reduction of industrial production and a reduction in industrial water use. Anyhow, results from figures 1 and 2 may serve as a clear example how unreliable data on water balance components may lead to inappropriate conclusions about the performance of water supply services.

Figures 3, 4, 5 and 6 represent the impact of the implemented activities, from the project's start (Activity 1) to its completion (Activity 7), to changes in the value of selected PIs for the Požarevac WDS and their uncertainty.

Figure 3: The influence of the implemented activities on changing the values of WR1 and Op23 and their uncertainty.

Figure 4: The influence of the implemented activities on changing the value of Op24 and Op26 and their uncertainty.

Figure 5: The influence of the implemented activities on changing the values of Op27 and Op28 and their uncertainty.

Figure 6: The influence of the implemented activities on changing Fi47 values and its uncertainty.

From the presented results it can be concluded that after implementation of all activities from 1 through 7, the uncertainty of all analyzed PIs has been reduced. It should be noted that the implemented activities have not led to an improvement in PI values, except for Op26 (apparent losses), but only to the reduction of their uncertainty.

The inefficiency of use of water resources WR1 has risen to 46% from an initial 27%, due to an increase in actual water loss. However, the uncertainty of this PI has decreased from an initial 84% to 6.5%. Namely, by installing high reliability flow meters at the source, higher values of the inflow of water were obtained, and as a consequence, the values of actual water losses in the WDS were increased.

The value of PI Op23 (water losses per connection) increased from an initial 570 l/conn.day to 767 l/conn.day, but the uncertainty of this indicator decreased from an initial 70% to 4.9%.

The PI Op24 value (water losses per mains length) increased from an initial 44,685 l/km.day to 57,814 l / km.day, but the uncertainty of this indicator decreased from an initial 70% to 4.6%.

The value of PI Op26 (apparent losses per system input volume) decreased from an initial 7.7% to 4.7%, while the uncertainty of this indicator remained practically the same (from an initial 40% it decreased to 37%). None of the activities carried out have had any effect on reducing the uncertainty of the value of apparent water losses, so their uncertainty remains high. To reduce the uncertainty of the volume of apparent water losses, other measures that are not covered by this work should be carried out.

The value of PI Op27 (real losses per connection) increased from an initial 443 l/conn.day to 696 l/conn.day, but the uncertainty of this indicator decreased from an initial 87% to 6.6%.

The value of PI Op28 (real losses per mains length) increased from an initial 44.802 l/km.day to 52.453 l/km.day, but the uncertainty of this indicator decreased from an initial 87% to 6.3%.

The Financial PI Fi47 (non-revenue water) has increased from an initial 39.9% to 51.7%, but the uncertainty of this indicator has decreased from an initial 58% to 4.6%.

Also, the value of the performance indicator ILI has increased, or worsened, for the same reasons. Implementation of all activities led to the increase of the estimated value of the ILI indicator from 7.7 to 10.5, but its uncertainty was significantly reduced from 88% to 9% (Babić et al., 2014). This PI is most commonly used as a measure of the effectiveness of the WDS from the aspect of water losses. Activity 7 (calibration of the mathematical model and determining the average pressure in the water supply system) is not necessary for determining the PIs and water balance components, except for determining the ILI indicator, since the value of the unavoidable annual real losses (UARL) indicator is directly proportional to the average pressure in the WDS.

From the results obtained after carrying out all the activities from 1 to 7, it can be concluded that locating all consumers and their entry into a database and GIS led to a significant reduction of uncertainty of input data for estimation of PIs and water balance components. By establishing a new database the number of monthly invoices were significantly increased (by almost 50%), as well as the number of registered meters (by about 20%).

Based on the presented PI values, it can be concluded that water losses in the Požarevac WDS are very high and the implementation of measures to reduce them is of the utmost urgency.

Conclusions

This paper presents the methodology for reduction of uncertainties of performance indicators and water balance components in water supply services, which is based on ISO/IEC guidelines. The methodology consists of a total of 7 activities applied in sequence; all aiming to reduce errors and uncertainties of data related to water distribution system elements and water flow measurements. The methodology was implemented in the Požarevac WDS, where water balance components, according to IWA methodology and selected performance indicators, together with their uncertainties, were estimated after each implemented activity. At the beginning of the study, the uncertainty of the input data, water balance components and the PIs were all extremely high. After implementation of the proposed methodology throughout the period from 2008 to 2013, uncertainty for all water balance components was significantly reduced, except for unbilled authorised consumption and apparent losses. However, it can also be concluded that after the implementation of all activities, the actual performance of the water supply has deteriorated as estimated values of the system input volume increased, authorised consumption and revenue water decreased while water losses and non revenue water (NRW) increased. This is a clear example of how unreliable data on water balance components may lead to inappropriate conclusions about the performance of water supply services. Regarding the effects of the implemented activities on uncertainty of the examined PIs, it can be concluded that implementation of all activities led to the significant reduction of uncertainty of all analyzed PIs. It should be noted that implemented activities have not led to an improvement in PI values, except for Op26 (apparent losses), but only to the reduction of their uncertainty. Further investigations are needed to properly address uncertainty of apparent losses.

Acknowledgement

The author is grateful to the Serbian Ministry of Education, Science and Technological Development for financial support throughout Project No TR-37010, and to the PUC "Požarevac Waterworks and Sewerage".

References

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