1. Introduction
Water losses have been identified as one of the leading problems common to any water utility in the world. High levels of losses can significantly affect future water resources availability, energy consumption associated to water production and distribution, overall quality of service to customers, water quality levels and operational costs and life of the assets. Depending on their nature, the International Water Association (IWA, London, UK) categorises water losses in two components [
1]: real losses and apparent losses. Real losses are mainly caused by leakage in pipes, valves, tanks, and other elements in the network. Apparent losses include the volume of water stolen by the users, the measuring errors of the meters and data handling errors. While apparent losses volumes are typically smaller than real losses, these two components become almost equal when making the comparison in terms of revenue loss caused by the utility. This is because a cubic meter of water lost in a leak in the network has a cost to the utility equal to the production cost. On the contrary, a cubic meter supplied to a customer that is not measured by the water meter has a cost to the utility equal to the retail price of the last cubic meter of water sold to that customer. In addition, in a properly managed water supply system, apparent losses are mainly caused by water meter inaccuracies. Consequently, the water utility’s revenue strongly relies on the actual measuring performance of installed water meters.
While the published International Standards on water meters [
2,
3] mostly specify the metrological and technical requirements of new meters, there is a lack of international standards defining how the metrological performance of the meters should be after installation. Only very few countries have specific legislation or standards in relation to the metrological requirements of used meters. In addition to this, the number of parameters that can affect the actual accuracy of a water meter in the field is not small. Thus, it is reasonable to assume that the metrological performance evolves over time—or with the amount of volume measured—depending on the working conditions, water quality, and design of the instrument itself [
4,
5]. Apart from that, there is not a standardised or widely accepted international procedure to calculate the overall metrological performance of the meters under real working conditions. Even more, studies related to the performance of installed meters are extremely difficult to find and frequently water companies keep them as confidential documents. All these factors in combination, make it difficult for water utility managers to estimate the actual impact of meters errors in their water balances and decide when is the optimal time to replace them [
6,
7,
8,
9].
By far, from all meters’ types used by water utilities, the most common ones are the ones employed to measure household consumption [
10]. Typically, around 90–95% of installed meters in a water utility are small diameter domestic meters and they measure around 70–80% of the total water consumption. Because of technical design limitations, domestic meters are not capable of registering the exact amount of water consumed by a customer. Depending on its construction technology [
11,
12], diameter, consumption characteristics of the customer, or type of water distribution system [
13,
14], each water meter has specific measuring limitations [
15,
16]. This means that a percentage of the water actually consumed by a customer may not be registered. If this is the case, the meter is said to be under-registering water consumption or have a negative error. Other times, some meter technologies, under certain working conditions, may show the opposite behaviour, that is, to register more water than the volume actually passed through the meter. Then, the meter is said to over-register water consumption or have a positive error. In either case, it is important to quantify the magnitude of these measuring errors to calculate the total amount of apparent losses.
For this analysis, a critical aspect to be considered is that the error of a water meter, despite the working principle used, varies with the flow rate passing through it. Typically, at low flow rates, measuring errors are more negative and sensitive to external variables [
17]. For medium and high flow rates, error variations are smaller and less sensitive to the magnitude of the flow [
16,
18,
19]. Thus, the difference between the amount of water registered by a meter and the actual volume used by the customer is also dependent on the consumption flow rates. The weighted error of a meter, defined as the relative difference between the actual consumption and the registered volume, can be obtained by combining the error curve of a meter and the consumption flow rates of the customer [
16,
20,
21]. Consequently, the weighted error is an indicator of the real, in the field, the overall metrological performance of a water meter when registering water consumption of a given user.
The main objective of this paper is to determine the weighted error of new and in-service single-jet domestic meters in order to provide information on the real field performance that can be expected from the meters installed in several water supply systems in the Spanish East Coast. More specifically, the study has focused on the analysis of two type of common single-jet domestic meters. The work has been conducted in collaboration between ITA-UPV (Universitat Politecnica de Valencia, Valencia, Spain) and FACSA (Sociedad de Fomento Agricola Castellonense, Castellón, Spain), one of the largest water supply companies in Spain.
Although the results cannot be directly extrapolated to other water utilities—due to the numerous factors affecting meters accuracy degradation—this work provides water meter managers with a reference of the methodology to be used in the estimation of the measuring errors. It can also provide a sense for an order of magnitude of the accuracy degradation rate of single-jet domestic meters and the procedure to identify the best approach for modelling their actual weighted error degradation. For the particular case of the water systems analysed, the results will be used in the future by FACSA to improve meter selection and to obtain a more accurate estimation of the actual level of apparent losses, revenue decay and calculation of the optimal replacement frequency of the meters [
20,
21,
22,
23,
24,
25].
4. Conclusions
This paper describes the results obtained from a work that was conducted during the past years in coordination with a water utility in Spain. The purpose of the study was to obtain the real degradation rates of the weighted error for two types of single-jet domestic water meters that are being used by FACSA in several water distribution systems and shows if a procurement selection procedure should not be mainly based on the initial errors of the meters.
The analysis of the weighted error of the meters tested shows that the usual assumption, which considers a linear degradation with age or totalised volume, is only acceptable in some cases. In other cases, like for one of the meters under study, this simplification is not acceptable. This work proposes a modified regression model to estimate more accurately the evolution of the weighted error with age and totalised volume as single drivers.
Another frequent simplification when estimating the measuring error of installed meters is to carry out a univariate regression analysis, using age or totalised volume, of the degradation of the weighted error. These models consider only one variable as the drivers of the weighted error. However, univariate regression models may not be accurate enough to establish the real performance of ageing meters. For example, a degradation model that only takes into account age will provide the exact same estimation for the weighted error of meters installed in customers with different consumption rates. However, the presented work has found that there are significant differences in the weighted error of meters having the same age and different totalised volume.
To improve the estimation of the actual performance of the meters this paper has presented a multivariate analysis of the weighted error degradation rates. The aim is to quantify the combined effect of age and totalised volume on the weighted error of the meters. For this purpose, a non-linear model—applicable to the meter types under analysis—that takes into account the initial error of the meters and the simultaneous impact of age and totalised volume has been derived. The proposed degradation model calculates more accurately the weighted error of the meters measuring the consumption of those customers having extremely low or large consumption rates.
It has been found that, for the meters under study, the differences between the proposed multivariate model and the model using the totalised volume are smaller than the ones found for the model using the age of the meters as the driver for the weighted error degradation. Following this, it can be concluded that for the meters analysed, the totalised volume can provide a better approximation than age.
Finally, it is important to highlight that the results obtained for the particular meter types tested cannot be extrapolated to other water utilities as the parameters that may affect the weighted error of ageing meters may differ from those present in the water supply studied. In addition, in order to obtain an accurate approximation of the measuring errors of installed meters, all meter types need to be tested and analysed. Two meter types can behave completely different in a specific water system and the same meter type can present dissimilar ageing processes in two different water systems.