Impact of active night population and leakage exponent on leakage estimation in developing countries

An estimated 666 million people lack improved drinking water worldwide (Ritchie & Roser 2019); amid the Sustainable Development Goals, SDG 6 aims at ensuring available and sustainable water for all by 2030. Van den Berg (2014) reports that huge volumes of treated water are physically and commercially lost from urban water supply systems annually as earlier reported by Kingdom et al. (2008). This loss amounts to 45 million cubic meters daily, costs the world approximately $5 billion a year, and is sufficient to serve nearly 200 million people worldwide (Kingdom et al. 2006).

Global leakage rates reported by Kingdom et al. (2006) have been corroborated by many other researchers. Burst losses and leaks contributed 13% out of 39% non-revenue water (NRW) in Sana, Yemen, 43% out of 51% NRW in Pirot, Serbia and 44% out of 50% NRW in Blantyre, Malawi (Kofodya 2010; Al-Washali et al. 2018; Radivojević et al. 2020). 67% in Selangor State, Malaysia. 59% in Kazerun, Iran, between 25 and 60% in five Bosnia-Herzegovinian utilities, 92% in Kafubu, Zambia and 44% in Kampala, Uganda (Chiipathenga 2008; Kamani et al. 2012; Vučijak et al. 2013). The reasons for these huge losses may be technical, socio-political and economic.

Studies by Knobloch et al. (2014) and Farley et al. (2011) indicate that the steps in addressing the leakage problem are fourfold; identify how much is lost, where the losses occur, why they occur and how they can be reduced. To determine how much is lost, three methods, namely – water balance (Farley et al. 2011; Knobloch et al. 2014), minimum night flow (MNF) (García et al. 2006; Tabesh et al. 2009; Xin et al. 2014) and component analysis also known as the Burst and Background Estimates (BABE) (McKenzie 2003; Fanner & Thornton 2005; Özdemir et al. 2021), have been identified and have been applied to the case study network in Amoatey et al. (2018).

The challenge these methods pose is their application to water networks with inadequate data, thus compelling water utilities to assume International Water Association (IWA) established parameters that may be sensitive to estimated leakage due to differing local conditions (Amoatey et al. 2018; Negharchi & Shafaghat 2020). For example, the infrastructure condition factor (ICF) and burst flow rates, used in the BABE method, must be determined per particular networks. However, in most developing countries, these factors have not been established, thus IWA rates, which are based on UK water networks, are used. Therefore, there is a need for water utilities in developing countries to develop local factors and rates for leakage estimation (Amoatey et al. 2018).

Similarly, the MNF method estimates leakage as the difference between night leakage (Q_L) and customer night use (Q_CNU), multiplied by the hour day factor (HDF). The active night population (ANP), is the percentage of customers that use water at night between 12:00 midnight and 04:00 am while the HDF accounts for the pressure variations during the day. The parameters, Q_CNU and HDF depend respectively on the ANP and the leakage exponent (N1). Q_CNU is also known as legitimate Night Consumption (LNC) and presupposes that customers with toilet flushing systems within a particular water distribution network, contribute to night flows. However, some people do not use toilet flushing systems which called for categorization of night users. These toilet-flusing and non-toilet flushing categories of night users is reported in earlier studies (Amoatey et al. 2014, 2018). The leakage exponent on the other hand depends on the pipe material, pipe age and environmental conditions of the network. As pipes of certain material advance in age, their response to changes in pressure varies and this can influence leakage exponent (Cheung et al. 2010; Lambert & Thornton 2012; De Marchis et al. 2016). Therefore, its influence in the estimation of leakage using the MNF method is being investigated in this study.

The influence of water loss (and NRW) parameters has been anticipated and have been the reason for various adaptations, modifications and re-definition of key concepts based on local network situations reported in previous studies (Tabesh & Asadiani Yekta (2005); Tsitsifli & Kanakoudis 2010; Al-Washali et al. 2020; Negharchi & Shafaghat 2020). Al-Washali et al. (2020) intimated that these have led to the introduction of correction factors, uncertainty, normalization, recognition of intermittent supply for among others.

It must be indicated that much has been reported on factors influencing apparent losses than have been reported on real losses. Fontanazza et al. (2015) identified meter age, meter inaccuracies, metering and billing errors incorrect installation practices, lack of maintenance or calibration, incorrect meter type and class and incorrect meter sizing as crucial for accurate estimation of apparent losses. The authors modeled the effect of private water tanks on apparent losses and recommended the use of unmeasured flow reducers (UFR) in such areas. Earlier authors like Tsitsifli & Kanakoudis (2010), Arregui et al. (2006), Tabesh & Asadiani Yekta (2005), Rizzo & Cilia (2005), Thornton & Rizzo (2002); have reported same.

With respect to real losses, though must has been studied on how to estimate the amount of leakage, not much has been explored as regards the influence of the factors used in these methods. Amoatey et al. (2018) identified the factors that influence all three leak estimation methods without analyzing the influence of the factors. The only study that has assessed the influence of some leak estimation parameters using the MNF method is that of García et al. (2006). The authors explored the influence of average zone pressure (AZP), the and the MNF hour on the leakage level error and proposed guidelines to improve the assessment of daily leakage rates using the MNF method.

Amoatey et al. (2014, 2018) studies identifed to be crucial in the MNF procedure in developing country water networks and argues that, an assumption of the parameter may not depict the actual local situation and could lead to inaccurate estimation of losses, resulting in setting inaccurate water loss reduction targets. Negharchi & Shafaghat (2020) also investigated the influence of and N1 on the amount of leakage estimated using the BABE and MNF methods in a network where domestic customers use water tanks. The authors found that changing N1 by 0.1, alters the estimated leakage by 1%, while changing by one step, alters the calculated leakage by 14% although it is not clear what a step is in that study.

This study, therefore, seeks to investigate the influence of ANP and on and HDF respectively and how both parameters subsequently influence estimated leakages. This is necessary since in the case study network, there are no automatic meter reading (AMR) systems that help identify typical night users and key water uses are not yet installed in the water network.

Farley (2001) recommends an ANP of 6% and this has been adopted in several studies (Fanner & Thornton 2005; Tabesh et al. 2009). ANP is the percentage of active consumers who use water between 12:00–4:00 am. The typical activities range are flushing of toilets, use of faucets, showers and use of washing machines is known as (Fantozzi & Lambert 2012). This parameter has been known to differ for different water networks and countries. A summary of customer night use rates for different countries is documented in Amoatey et al. (2014) and updated by Negharchi & Shafaghat (2020).

Loureiro et al. (2012), identified social demographic factors such as property type, household size, daily habits of customers as well as technical, climatic factors and maintenance program of water utility as factors that influence and studied these extensively in Portugal. This makes the determination of ANP crucial for obtaining ⁠. Amoatey et al. (2018) identified three ways by which can be estimated but recommends using Automatic Meter Infrastructure (AMI) to identify the typical night uses and the active night population.

Fantozzi & Lambert (2012) carried out a study using smart metering systems in Australia and found ANP to be 3% confirming the fact that the recommendation to use 6% in earlier studies (Farley 2001; AL-Washali et al. 2019) might not be the same for all networks. This paper therefore posits that, some water networks especially in developing countries may have lower ANPs than the recommended 6% and the measured 3% (Fantozzi & Lambert 2012). Again, it is possible that with an increase in socio-economic activities coupled with the new way of working since the SARS-CoV 2 pandemic struck, ANP may be relatively higher in some networks than that found in the Fantozzi & Lambert (2012) study. Thus, it is imperative that water utilities know how far the leakage situation in the network is from reality. Since most developing country networks do not have AMI or smart metering systems, and not all consumers use toilet flushing systems, it is essential to investigate what relative error exists with the choice of an ANP rate.

Another parameter under investigation is the sometimes called night day factor (NDF) is a dimensionless parameter that presupposes that leakage and pressure are related, thus, by controlling pressure, water losses can be reduced (García et al. 2006; Cheung et al. 2010; Al-Washali et al. 2019; Özdemir et al. 2021). It is known from the Morrison et al. (2007) study that, gravity-fed networks and low-pressure gravity systems usually have less than or equal to 24 hours per day due to high frictional head losses. depends on and are estimated in the UK to range between 15 and 30, with an average of 22, and between 18 to 22 in South Africa (García et al. 2006; Cheung et al. 2010; Lambert & Thornton 2012). In a study in Kayseri, Turkey, Özdemir et al. (2021) found HDF to be 22.5.

Since shows the interdependency of leakage on pressure, theoretically, leakage rates in water distribution systems vary with the square root of pressure (Lambert 2001; Cheung et al. 2010). Practically, however, tests in various countries have yielded higher N1 values due to changing flow conditions (laminar, transition or turbulent) and changing orifice area and size in terms of holes, slots or cracks of leaks (Lambert 2001). The determination of N1 is specific to any distribution network and is obtained from field studies by gradually reducing flow into a section of the network and recording changes in pressure over a period of time (Lambert 2001; Tabesh & Asadiani Yekta 2005; García et al. 2006; Thornton et al. 2008; Cheung et al. 2010). values have been found to typically range from 0.5 to 2.5 (García et al. 2006; Tabesh et al. 2009; Cheung et al. 2010; Negharchi & Shafaghat 2020; Özdemir et al. 2021) depending on pipe material and level of leakage. The more rigid the pipe material, the closer the is to 0.5. Networks with mixed materials range between 0.5 and 2.5. An established value of 1.15 is reported in Japan, 1.13 in UK distribution systems and close to 1.5 in Australia and New Zealand systems (Lambert 2001; Thornton & Lambert 2005; Lambert & Thornton 2012). Schwaller & van Zyl (2015) found N1 values between 0.46 and 1.67, with the vast majority of values lying between 0.5 and 1.5 in a model of the distribution of individual leaks and their parameters. It must be indicated therefore that the effect of age and material type of pipes has an indirect influence on of the network (De Marchis et al. 2016).

This paper seeks to establish the influence of ANP in the and in HDF parameters on the estimated leakage volume in developing country water networks. It emphasizes the need to establish these parameters for particular networks. The relative error associated with an assumed ANP and is investigated to establish how changes in these parameters influence leakage volumes in a network. It is expected that water utilities in developing countries will adopt localized parameters to determine actual leakage levels so as to be able to accurately determine key performance indicators and set leakage reduction strategies.

The Baifikrom water network is located mainly in the Mfantsiman Municipal Assembly in the Central Region of Ghana and was selected as the study area for this work because the network had been zoned, expanded and rehabilitated. It supplies 32 communities with a population of about 122,000 (AVRL 2008), some of which are rural over an area of approximately 250 km². The design per capita consumption rates range from 30–75 litres/capita/day (Adombire 2007). The total demand is 318 m³/h. Pipes are made of Asbestos Cement (AC), High Density Polyethylene (HDPE) and Polyvinyl Chloride (PVC) making about 150 km in length.

The pipe sizes range from 75–500 mm (AVRL 2008). The network (Figure 1) has approximately 5,700 service connections and 85% customer metering. Water is pumped from the Treatment Plant (WTP) into 4 reservoirs sited at the highest points (on hills) within the supply area. Water then flows under gravity from these reservoirs into the towns and communities. Rural communities are mainly served through public standpipes as some cannot afford a water meter connection. Also fixed outlet pressure reducing valves (PRVs) set at pressures between 10 and 30 m reduce flow to communities that branch off from the transmission mains.

Out of the 32 towns, 3 of them – Mankessim, Saltpond and Anomabo – are the most vibrant, with the remaining being rural farming and fishing communities. There is the market at Mankessim where vibrant commercial activities take place mainly during the day. It is the most populous town with a few commercial and rural banks. Saltpond and Anomabo have much smaller markets where fish, sea foods and salt are major commodities. There are a number of Secondary/High schools in these three towns. These towns are the most likely to have a section of their populace using toilet flushing systems. Most rural communities rely on public stand pipes and that accounts for the high number of stand pipes in this water network.

According to Mfantsiman Municipal Council (2012) assembly, only 10% of households use toilet flushing systems in this network. For this reason, the MNF procedure was modified to make it applicable to this network in an earlier study (Amoatey et al. 2018). The Baifikrom water network reports annual non-revenue water (NRW) of about 50% and this had not been broken down into its major components – leakage (physical) and apparent (commercial) losses (GWCL 2014). The NRW of the Baifikrom network is similar to other networks like Mwanza, Tanzania, Sana'a, Yemen and Zarqa, Jordan (Al-Washali et al. 2019).

After 3 months, the minimum night flow rate for the network was measured to be 40 m³/h. N1 was found to be 2.4 resulting and an HDF of 20 obtained from pressure measurements taken over three weeks (Amoatey et al. 2012). Because the pipe materials in the case study network are 70% plastic, an of 1.0 was theoretically expected (García et al. 2006; Lambert & Thornton 2012; De Marchis et al. 2016). In analyzing the relative error of leakage estimated for for each ANP rate considered, a range of values 0.5 to 2.5 in steps of 0.5 is considered.

was estimated for two categories of night users and summed up in the same way as in the pilot study reported by Amoatey et al. (2014). Total Q_CNU was estimated for 1–6% ANP and used to estimate leakage. The relative error associated with each ANP rate was computed for ⁠, range of values based on the modified MNF method is assessed (Amoatey et al. 2014, 2018).

This enables water utilities to see how much ANP and contribute to the volume of leakage. Therefore, in this study, leakage was estimated for a 1–6% range of ANP and for each N1 step in the range, as indicated earlier. As indicated earlier, the range of ANP values considered, testing the uncertainty of in the range appears realistic for water networks around the world (Farley 2001; Fantozzi & Lambert 2012). The sensitivity of ANP for each value in the range considered was determined by assuming a rate of 3%. The absolute error for the volume of leakage estimated determined for each ANP rate is compared with that of the assumed rate (Reuter & Liebsche 2008; Saltelli et al. 2008).

Ikonen (2016) proposed a one-factor-at-a-time (OAT) method, which determines the change in model output values that results from modest changes in model input values. However, since both ANP and are necessary at the same time in the MNF method, both parameters interact to affect the precision of the amount of leakage estimated. In such a case, Loucks & Van Beek (2005) proposed a multivariate linear analysis to evaluate the approximate impact. This approach, however, requires a definition of the probability distributions of the parameter sets (N1 and ANP) which is difficult to establish in this study.

The challenge of finding other methods which could be confirmatory and more robust can be identified as a limitation of this study. The authors will consider some mathematical theorems and assumption that could explain such problems if the future. Many studies have been conducted on factors that influence accurate estimate of apparent losses (Thornton & Rizzo 2002; Tabesh & Asadiani Yekta 2005; Rizzo & Cilia 2005; Arregui et al. 2006; Tsitsifli & Kanakoudis 2010) but for real losses, only García et al. (2006) and Negharchi & Shafaghat (2020) have studied some leak estimation parameters, the later however, used actual measurements and no uncertainty analysis in particular.

The results presented in Table 1 below have 3 parts as indicated by the solid lines, long dashes and short broken lines. The first part indicates the computation of per capita and for the entire population in the network for the two categories of night users – toilet flushing and non-toilet flushing customers. Following the procedure described earlier, for toilet flushing customers was found to range between 0.16 L/h and 0.71 L/h, whereas non-toilet flushing customers ranged between 0.03 L/h and 0.08 L/h respectively for ANP of 1%–6%. The per capita obtained was reported and discussed in Amoatey et al. (2014) study in comparison with similar rates from Uganda Mutikanga et al. (2010); and ASEAN region (Fantozzi & Lambert 2012).

The for the population per category was then computed and summed up, and the total for 3% ANP was found to be 9,845.4 L/h. estimates obtained were compared with a similar study in Kampala, Uganda and found to be realistic (Amoatey et al. 2014, 2018). These were subsequently used together with the measured night leakage and HDF to determine the leakage volume. The total daily leakage indicated by the region with long dashes was computed for each ANP over a range of five with corresponding HDF values.

Leakage volume for Baifikrom network for of 2.4 which translates into an HDF of 20 was found to be 663,401 L/day at 3% ANP (shown by the circled value). The third region (indicated by the short dashes), contains the percent leakage relative to the amount supplied for each (with corresponding HDF) over 1–6% ANP. The percent leakage for each ANP for the expected theoretical is between 9-14% and for the field-determined ⁠, leakage ranges between 8 and 13% of the supplied volume (see Table 1). Therefore, for an ANP of 3%, and of 1.0, leakage is 12.4%, which indicates that leakage in the Baifikrom network is relatively lower in comparison with total leakage. The differences in leakage obtained per ANP rate reveal the importance of establishing actual rates for every network.

Considering that water loss for the entire study network is about 50%, the amount of leakage estimated appears to be small (Amoatey et al. 2018) even though similar in comparison with Al-Washali et al. (2019) findings for Zarqa (Jordan) and Mwanza (Tanzania) with average leakage of 15 and 11% respectively as against 66 and 46% NRW. It can therefore be seen that apparent losses are about three times higher than physical losses similar to other reports from Asia and Africa (Lievers & Barendregt 2009; Mutikanga et al. 2010).

Again, from Table 1, the relative error associated with the volume of leakage estimated for the range of ANP and N1 values using 3% and 1.5 as the nominal values respectively is indicated by the long dash double dot area. It can be seen that a 1% higher or lower ANP results in an 8% under-or overestimation of leakage. This implies that if AMR reveals that the actual ANP for the case study network is 2% instead of the 3% assumed nominal, the amount of leakage overestimated by 8% of the assumed nominal of 12%.

Although the Negharchi & Shafaghat (2020) did not investigate active night population in particular, the authors found that changing the measured legitimate night consumption by one step alters the calculated leakage by 14%. Again, because the authors were also interested in the influence of private water tanks on ⁠, the results were 14 times higher than the 1.7 litre/connection/hr recommended in the UK Water Industry (1994) report. In a summary of different customer night consumption values presented in Amoatey et al. (2014), it can be realized that studies in Ottawa, Canada, Malaysia were also higher than 1.7 lit/connection/hr. Again, though the premise of the Negharchi & Shafaghat (2020) study is not directly comparable with this study, it buttresses the fact that every water network is characteristic, and therefore cannot adapt parameters established elsewhere.

Similarly, the relative error associated with of 1.5 as the nominal leakage exponent results in a maximum of 4% over or underestimation for a 0.5 lower or higher step respectively. It can be realized that there is an increasing linear relationship between a relative error of ANP and irrespective of the assumed rate confirming the findings of García et al. (2006) for ⁠. With actual measurements, Negharchi & Shafaghat (2020) found that a 0.1 change in results in a 1% change in leakage. Comparing the results of this study with the Negharchi & Shafaghat (2020) work, the results are similar, in that, since a linear relationship is linear relationship exist between ⁠, and leakage in this study, it can be inferred that a 0.1 step results in a 0.8% leakage which is approximately 1%. The García et al. (2006) study however, reports a 10 times greater error for a ±10% change in than which is higher and probably more sensitive than this and the Negharchi & Shafaghat (2020) study. This supports the fact that networks differ and respond differently depending on the type of leak(s) predominant within the network.

With the arguments above, it can be seen that the accuracy of both parameters is crucial for quantifying leakage in water networks and this should be ensured by water utilities. Accurately estimating leakage has technical and research implications in that water utilities around the world are striving for efficiency in their services and in the management of the utility. In view of this, water utilities calculate key performance indicators (KPI) and set targets for leakage reduction and investment priorities. This makes the water utilities comparable with others around the world.

Again, since water loss is made up of leakage and apparent losses, the water utility can plan how to tackle apparent losses while it reduces leakage. For this reason, over or underestimating leakage further affects leakage reduction targets, and planning of maintenance investment priorities. Further research will consider a survey of ANP in the Baifikrom study network will be conducted to reduce leakage estimation uncertainties.

This paper investigated the relative error in leakage estimation using the minimum night flow method in the Baifikrom water network where some parameters have not yet been established and localized. Changes in the amount of leakage when a range of ANP rates for calculating and N1 values for estimating HDF was investigated. It was found that a linear relationship exists between the relative error of ANP and N1, although ANP is more crucial. It is recommended that water utilities must establish localized ANP and values for accurate leakage estimation in water networks.

All relevant data are included in the paper or its Supplementary Information.