Analytical scaling relations to evaluate leakage and intrusion in intermittent water supply systems

Abstract

Intermittent water supplies (IWS) deliver piped water to one billion people; this water is often microbially contaminated. Contaminants that accumulate while IWS are depressurized are flushed into customers' homes when these systems become pressurized. In addition, during the steady-state phase of IWS, contaminants from higher-pressure sources (e.g., sewers) may continue to intrude where pipe pressure is low. To guide the operation and improvement of IWS, this paper proposes an analytic model relating supply pressure, supply duration, leakage, and the volume of intruded, potentially-contaminated, fluids present during flushing and steady-state. The proposed model suggests that increasing the supply duration may improve water quality during the flushing phase, but decrease the subsequent steady-state water quality. As such, regulators and academics should take more care in reporting if water quality samples are taken during flushing or steady-state operational conditions. Pipe leakage increases with increased supply pressure and/or duration. We propose using an equivalent orifice area (EOA) to quantify pipe quality. This provides a more stable metric for regulators and utilities tracking pipe repairs. Finally, we show that the volume of intruded fluid decreases in proportion to reductions in EOA. The proposed relationships are applied to self-reported performance indicators for IWS serving 108 million people described in the IBNET database and in the Benchmarking and Data Book of Water Utilities in India. This application shows that current high-pressure, continuous water supply targets will require extensive EOA reductions. For example, in order to achieve national targets, utilities in India will need to reduce their EOA by a median of at least 90%.

Fig 1. Single node equivalent of an IWS.

We model the system or sub-system as an equivalent node, with pressure head H, average external fluid pressure H_C, flow to customers Q_d, and leakage flow Q_L; A is the equivalent area of pathways for leakage and f_CA is the equivalent area for intrusion.

Fig 2. Supply duration’s effect on intruded fluids.

Compare an initial system (top panel) with supply period duration t⁰, customer demand volume V_d, and contaminant intrusion rates Q_C and Q_CF during the supply and non-supply periods, to the same system (bottom panel) if the supply period duration is lengthened (to t*). If all-else is held constant, Q_C and Q_CF are also constant.

Fig 3. LR during the flushing phase from increased supply duration and reduced EOA, separately.

The LR during flushing attributable to increased supply duration (thick black line and square dot), and due to the necessitated reductions in EOA (colored dashed curves), each plotted separately. Three levels of allowable leakage increases are shown: no increase (pink/upper curves), a 50% increase in physical losses (i.e., $\frac{l}{pN}=0.5$) (green/middle curves, and circle), and a 100% increase in physical losses (blue/lower curve). Final durations of 15, 21, and 23.75 hrs/day are shown in the top (a), middle (b), and bottom (c) panels, respectively. The text’s example utility is also shown (square and circle).

Fig 4. Key scaling relationships governing the risk of intrusion.

Fig 5. Required EOA reductions in BDBWUI.

Our model suggests that increasing the supply duration to 23.75 hrs/day and the pressure to 17m will require utilities to reduce their EOA by a fraction (y-axis) that depends on how much of their current NRW is physical loss (p) and their allowed leakage increases (l). Box plots summarize these required EOA reductions under scenarios i) and ii) (i.e., a) $\frac{l}{p}=0.3$ and b) $\frac{l}{p}=0.02$).

Fig 6. Required EOA reductions in IBNET.

Our model predicts that increasing the supply duration to 23.75 hrs/day will require utilities (grey dots) to reduce their EOA by a percentage (y-axis) that depends on their initial supply duration (x-axis) and the ratio of allowed leakage increases (l) to the percent of their current NRW that is leakage (p). We plot each utility under scenarios i) and ii) (i.e., a) $\frac{l}{p}=0.3$ and b) $\frac{l}{p}=0.02$). For initial supply durations within a 1-hour span (e.g., 4.5-5.5 hrs/day), the 5th (red/upper line), 50th (i.e., median, green/middle line), and 95th (blue/lower line) percentiles are smoothed into the displayed curves.

Fig 7. Which improvements reduce the risk of intrusion?

For each utility (grey dot) in our filtered IBNET and BWBWUI database, we plot the predicted log reduction (LR) of intruded volume in steady-state (a & b) and flushing (c & d) phases, attributable to increasing the supply duration to 23.75 hrs/day (thick black line) and attributable to the necessitated EOA reductions. For steady-state (a & b), the effects are considered together (solid thin lines), but for the flushing phase (c & d), the effect of EOA reduction is shown separately (dashed thin lines). We plot each utility under scenarios i) and ii) (i.e., $\frac{l}{p}=0.3$ (a & c) and $\frac{l}{p}=0.02$ (b & d)). For initial supply durations within a one-hour span (e.g., 4.5-5.5 hrs/day), the 5th (red/upper line), 50th (i.e., median, green/middle line), and 95th (blue/lower line) percentiles are smoothed into the displayed curves.

Fig 8. LR from pressure-necessitated EOA reduction.

As utilities (dots) in the filtered BDBWUI database increase supply pressures from their initial pressures (x-axis) to 17m, the proposed model suggests that EOA must be reduced. Different EOA reductions are required under scenarios i) and ii) (i.e., a) $\frac{l}{p}=0.3$, and b) $\frac{l}{p}=0.02$). These reductions in EOA are predicted to translate to LR in the intruded volume (y-axis).