Javier González

Residence time (or water age) is often used as a surrogate indicator of water quality in water distribution networks. Water age depends on the system design and associated demands, which are stochastic in nature, so the identification of critical areas (areas prone to high water ages) must be addressed from a probabilistic perspective. A systematic approach for the STATistical characterization of Water AGE (STATWAGE) has been recently presented in the literature. It has proved that Bottom-Up (BU) demand allocation strategies, which acknowledge the pulsating nature of water demands, are associated with greater water age variance than more conventional Top-Down (TD) approaches, which rely on average consumption patterns. The aim of this paper is (i) to assess if there are any laws of behavior that can explain the difference in variance between STATWAGE-BU and STATWAGE-TD by relying on temporal variability levels, and (ii) if such behavioral laws exist, to propose a systematic approach to simplify the estimation of this additional variance and thereby complement STATWAGE-TD results. This paper demonstrates that these differences are related to the short-term variance of network flows, and a new complement (Short-Term Incremental effect over Water AGE Variance, STIWAGEV) is here presented to consider their effect. The STATWAGE-TD + STIWAGEV approach is a potentially meaningful contribution for effectively quantifying the statistical properties of water age without having to rely on complex BU models and/or high-resolution data. Therefore, this framework constitutes the first step towards developing a systematic methodology for accurately and affordably identifying critical areas.

Free chlorine residual is the most widely adopted disinfectant residual in water supply systems. Chlorine is usually applied at treatment works, but it decays as water flows and spends time within the network. Chlorine decay is the result of a bulk and a wall decay component. Bulk decay may be considered invariable through the pipe network (it only depends on water composition) and is often characterized at the entrance to the system through bottle tests, which measure chlorine evolution over time in a laboratory environment to then adjust a model (dependent on one or more coefficients) that represents its behavior. Previous studies have acknowledged that the bulk decay coefficient varies widely and that free chlorine measurements are subject to measurement errors, but they have not quantified the impact of these errors on the bulk decay coefficient. The aim of this paper is to provide a methodology that statistically fits chlorine’s bulk decay coefficient based on bottle test results, with appropriate management of uncertainty effects. The proposal is to use state estimation techniques, which combine free chlorine measurements and system knowledge (in this case, a first-order bulk decay model) to provide the most likely chlorine behavior and its associated uncertainty. This approach goes one step beyond previous studies, which report only a single value of the bulk decay coefficient without accounting for randomness, and thus fail to assess true variability, leading to unrepresentative comparisons. Results for water samples from different sources demonstrate the importance of controlling the fitting process through state estimation to understand and compare the bulk decay coefficient.

Water age or time of residence is frequently adopted as surrogate indicator for water quality in water distribution networks. High water ages, which are expected in terminal branches and meshed areas with low renovation rates, are associated with different physical, chemical and/or biological issues. However, the identification of critical areas is complex because it depends on the system design and associated demands, which are stochastic in nature. This work aims to develop a methodological framework to statistically characterize water age in water distribution networks. A detailed analysis of residence times is here performed at a parametric terminal branch inspired in a real case study. Water age statistical properties (mean and variance) are computed in this work from Monte Carlo simulations and compared for different network sizes, types of nodes and demand allocation strategies. Moreover, volumetric probabilistic curves for the Supplied Water AGE (SWAGE plots) are here defined and generated at each node. The practical interest of SWAGE plots (which provide the ratio of supplied water volumes with age above different threshold values) for the identification of critical areas justifies the necessity of defining a systematic framework for the STATistical characterization of Water AGE (STATWAGE). The potential and difficulties associated with the real implementation of STATWAGE are here discussed.

The quality of water supplied through water distribution systems is traditionally assured through sampling of different physical, chemical, and biological parameters at the exit of water treatment works and at different locations within the network. However, sampling is periodic and does not capture the complex processes that take place within the network over time and space. The time of residence of the resource within the network (also called water age) has been used in the past as surrogate indicator for water quality (Machell and Boxall, 2012). As water age increases, water quality parameters tend to worsen (Machell and Boxall, 2013). This is more likely in terminal and meshed areas with low renovation rates (high water age). This work presents a detailed analysis of residence times at a terminal branch. This benchwork branch is inspired in the real topology of water connections at several dead ends in a water supply network in Spain. Stochastic demands are simulated per water connection thanks to a demand model inspired in SIMDEUM (Blokker et al., 2010). Demands are then used to run a hydraulic and water quality model with high resolution. Different metrics are then computed to probabilistically assess water age within the branch. These metrics are useful to identify topologies that are especially problematic.Acknowledgements:The authors would like to thank the financial support provided by the Spanish Ministry of Science and Innovation - State Research Agency (Grant PID2019-111506RB-I00 funded by MCIN/AEI/10.13039/ 501100011033; Grant TED2021-131136B-100 funded by MCIN/AEI/10.13039/501100011033) and Junta de Comunidades de Castilla-La Mancha (Grant No. SBPLY/19/180501/000162, funded by Junta de Comunidades de Castilla-La Mancha and ERDF A way of making Europe).References:Machell, J. and Boxall, J. (2012) Field studies and modeling exploring mean and maximum water age association to water quality in a drinking water distribution network. Journal of Water Resources Planning and Management, 138(6), 624-638, https://doi.org/10.1061/(ASCE)WR.1943-5452.0000220Machell, J. and Boxall, J. (2013) Modeling and field work to investigate the relationship between age and quality of tap water. Journal of Water Resources Planning and Management, 140(9), 04014020, https://doi.org/10.1061/(ASCE)WR.1943-5452.0000383Blokker, E.J.M., Vreeburg, J.H.G. and van Dijk, J.C. (2010) Simulating residential water demand with a stochastic end-use model. Journal of Water Resources Planning and Management, 136(1), 19-26, https://doi.org/10.1061/(ASCE)WR.1943-5452.0000002

The effect of different temporal (from seconds to months) and spatial aggregation scales (from individual users to full urban areas) on water demand behavior has been explored to a limited degree. The effort described here extends those works by evaluating the scale effects of residential water consumption in a unique US data set that covers 10,000 households with a 1-gallon (3.79 L) hourly resolution over 2 years. A preliminary data analysis and a sequential Principal Component Analysis (PCA) is carried out to assess the effect of different temporal (weekly, daily, hourly) and spatial aggregation (individual meters and groups every 10, 100 and 1,000 meters) levels on demand. Results show that individual users act very differently from each other, and individual consumer variability is only canceled out when a significant number of households are aggregated. The implications of this finding are assessed from a hydraulic modeling perspective as the spatiotemporal scale of measurements may condition the type of analysis that can be carried out in practice. However, additional work is needed to explore the point at which it may be worth embracing a micro (per fixture/household) or a macro (per node/network) approach for different purposes.

TEmporal Scale SIgmoid Curve (TESIC): A tool to characterize short-term demand variability at water supply systems