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Technical Papers
Jun 3, 2024

Economically Optimal Leak Management: Balancing Pressure Reduction, Energy Recovery, and Leak Detection and Repair

Authors: Charles Hammond [email protected], Robert Good [email protected], and Frank Loge https://orcid.org/0000-0002-8264-7021 [email protected]Author Affiliations
Publication: Journal of Water Resources Planning and Management
Volume 150, Issue 8
https://doi.org/10.1061/JWRMD5.WRENG-6428
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Abstract

Maximizing the net economic benefits of leak management programs provides the most value to water utilities and their customers. Leak management programs with alternative objectives (e.g., to “break even” or to maximize leak reduction) are not necessarily the most efficient use of resources. Combining hydraulic modeling with principles of economics and using a real distribution system to provide a case study, we present a methodology for maximizing the net economic benefits of a leak management program consisting of leak detection and repair activities and pressure management interventions. The optimization results include recommended leak detection and repair intervals for individual district metered areas, optimal siting of both pressure reducing valves and pumps-as-turbines (PATs), and modifications to the distribution system’s connectivity to isolate high-pressure areas. The case study results indicate that 10% to 11% of the system’s current energy use can be recovered by PATs and that the avoided leakage over the study period is equivalent to 13% to 23% of the system’s current customer demand. While leak detection and repair and pressure management are more commonly considered independently, this analysis demonstrates the feasibility of including their interdependencies when optimizing a leak management program, resulting in more useful recommendations.

Introduction

Safe, reliable, and affordable potable water is essential for social and economic prosperity. In many regions of the world, growing populations and arid conditions are straining water resources (Kunkel 2016; Liemberger and Wyatt 2019; Liu et al. 2022; Tzanakakis et al. 2020). In addition to efforts to reduce water consumption through conservation, water suppliers are obligated to accountably and efficiently manage their water resources (Kunkel 2016). The amount of water lost by water suppliers is known as nonrevenue water and consists of two types of losses: real and apparent (Sturm et al. 2008). Real losses include leaks, overflows, and blow-offs anywhere in the distribution system (Sturm et al. 2008). Apparent losses consist of water lost to theft or illegal use and water that is not physically lost but that fails to produce revenue due to inaccurate metering or other data errors (Sturm et al. 2008). Reducing real losses through leak management represents a significant opportunity for water suppliers to minimize waste and increase the supply of water available to customers (Rupiper et al. 2022). For example, water audit data for 882 water suppliers in the United States revealed that water lost to leaks on average accounted for 17% of the total water produced, ranging from 1% to 55%, depending on the supplier (Rupiper et al. 2022). Globally, leakage rates may range from approximately 4% in Amsterdam to 65% in Tuxtia, Mexico (OECD 2016). Awareness of the need to monitor and mitigate leak losses is now widespread, with many countries considering measurement and control programs (Rupiper et al. 2022).
The three main activities that water suppliers may use to reduce leak losses are leak detection and repair, pressure reduction, and preventative pipe replacement (Lambert and Fantozzi 2005). Although necessary for long-term maintenance of a water distribution network, preventative pipe replacement is generally not cost-effective from the perspective of reducing leaks (Rupiper et al. 2022; Trow and Farley 2004). Recent work suggests that pressure reduction and leak detection and repair may be the most affordable ways to increase the available water supply compared with common alternatives (e.g., purchasing additional water) (Rupiper et al. 2022). Leak detection is a broad field of research that has led to the development of technologies that take advantage of acoustic, pressure transient, vibrational, flow, and other types of data to locate leaks in water distribution networks (Hu et al. 2021). For example, acoustic methods may use ground microphones, leak noise correlators, and noise loggers, while other methods include ground-penetrating radar and thermal infrared imaging (Fan et al. 2022). After detecting and locating leaks, the water supplier may take corrective action to prevent further water loss.
Pressure management aims to reduce pressures to the minimum levels required to provide adequate service. Water suppliers may be required to provide higher pressure than necessary to many customers to ensure that all service connections receive adequate pressure. For example, customers at lower elevations will likely receive higher pressure than customers at higher elevations within a district metered area (DMA), which is sometimes referred to as a “pressure zone.” Alternatively, pump stations may sometimes provide more pressure than is necessary to an entire DMA for other reasons. In either case, greater pressures result in greater leak losses, which water suppliers have traditionally managed using pressure reducing valves (PRVs) placed at strategic locations within the distribution system. However, the energy dissipated in PRVs can instead be captured by pumps operating in reverse as turbines (PATs) with an attached generator. Depending on the energy recovery potential, PATs may sometimes be more economical than PRVs. Determining where to place PRVs and PATs within a distribution network has been the focus of significant recent research efforts. Research objectives have included maximizing energy recovery (Carravetta et al. 2012; Corcoran et al. 2016; van Dijk et al. 2022; Fernández García and Mc Nabola 2020; Giugni et al. 2014; Lima et al. 2017a; Moazeni and Khazaei 2021; Morani et al. 2023; Telci and Aral 2018); multiobjective optimization of energy recovery and leak reduction (Bonthuys et al. 2020; Ebrahimi et al. 2021; Fecarotta and McNabola 2017; Morani et al. 2021; Sambito et al. 2021); cost–benefit analysis (Carravetta et al. 2014; Fecarotta et al. 2015); case studies (Novara and McNabola 2021; Patelis et al. 2017; Su and Karney 2015); PAT selection, design, and operation (Alberizzi et al. 2019; Amelio et al. 2020; Bideris-Davos and Vovos 2023; Fontanella et al. 2020; Lima et al. 2017b; Lydon et al. 2017; Pugliese and Giugni 2022; e Souza et al. 2023; Stefanizzi et al. 2020); and capacity assessment (Kao et al. 2022). Although previous studies have used economics and hydraulic modeling to determine the optimal placement of PRVs and PATs, here we recognize that, because the amount of water saved by a leak detection and repair program is dependent on the operating pressure, the placement of PRVs and PATs should take place within the context of a more complete leak management program.
To provide maximum value to customers, leak management programs should be operated at the economically efficient level of losses (i.e., the level of leakage beyond which leak reduction is no longer the best financial choice for increasing the supply of available water) (Rupiper et al. 2022). To achieve this, the net benefits provided by leak reduction efforts should be maximized. While the economic model given by Rupiper et al. (2022) is adequate for making general comparisons and producing broad conclusions involving a large number of organizations, we suggest several modifications to improve the usefulness and rigor of the model when applied to a specific water distribution system. First, rather than assuming baseline pressure reduction benefits and independently optimizing leak detection and repair operations, we optimize both activities simultaneously and include their interdependencies. Second, we utilize the hydraulic model of a real water distribution system to propose detailed modifications to the distribution system to reduce pressures. Third, we consider the use of PRVs and PATs for pressure reduction and energy recovery. We apply these methods to a portion of the distribution network operated by Marin Municipal Water District (hereafter referred to as Marin), a water supplier serving 191,000 people in Northern California, and provide the results as a case study for other utilities seeking to manage their leaks more efficiently and economically through optimizing the placement of PRVs and PATs and the frequency of leak detection surveys.

Methods

Determining the financially optimal leak management policies and operations requires economic and engineering principles. Hydraulic modeling is required because the costs and benefits of leak detection and repair and pressure reduction are interdependent. For example, if the pressure in a DMA is reduced, the benefits of surveying for leaks are reduced. Conversely, if leak detection and repair are performed more frequently, the benefits of pressure reduction are reduced. Hydraulic modeling accurately describes how such modifications to system operation impact the results. Economic principles are necessary to understand the true costs and benefits of leak management activities so that economically efficient solutions may be found.

Hydraulic Modeling

Hydraulic models of water distribution systems solve systems of equations based on the principles of energy and mass conservation to estimate variables of interest to engineers and operators, including flow, velocity, and hydraulic head and provide valuable assistance for the planning, design, and operation of hydraulic pipelines (Walski et al. 2013, 2020). Marin’s distribution network conveys approximately 83,279  m3 (2.2×107  gal) of water per day through 1,461 km (908 mi) of mains and approximately 64,000 service connections. For this analysis, a hydraulic model for the city of Sausalito, in Marin’s southwest service region, was constructed using EPANET Version 2.2, the industry-standard hydraulic modeling simulation toolset (Rossman 2000; USEPA 2020). The model was skeletonized and calibrated to a seven-day period in the summer of 2019, identified by Marin as typical and without operational disturbances or changes. The model includes 33.67 km (20.92 mi) of distribution pipes with an average diameter of 20.3 cm (8 in.) and is supplied by a single reservoir representing the rest of Marin’s network. A total of 19 valves, 12 pumps, and 8 storage tanks are distributed within the model to provide water service to 904 junctions.
Elevations of junctions in the Sausalito model range significantly from a minimum of 2.7 m (9 ft) to a maximum of 300.8 m (987 ft), with an average of 67.4 m (221 ft). Average service pressures range from 614 to 676 kPa (89 to 98 psi), and junction pressures in the model agree with known hydrant pressures within ±34.5  kPa (±5  psi) for 90% of the hydrants and within ±69  kPa (±10  psi) for the rest, excluding a small number of outliers, which could not be explained with the modeled hydraulics. Customer water demand was generated from monthly bills and assumed time-series patterns for each customer class such that total usage matches the observed hourly total system water production. Between the valves and pumps, a total of nine isolated service regions, or DMAs, were identified by their connectivity. Valves, pumps, other infrastructure, and their associated properties (e.g., energy demand or production) are considered as belonging to a DMA only if they are upstream. Each DMA has its own service pressure range, which varies principally based on elevation and distance from the nearest storage tank. A winter 2019 simulation was performed using the same model calibrated for summer 2019, reducing the system-wide demand multiplier from 1.0 to 0.573, which was calculated by dividing the total volume of water sold in February of 2019 by that of August of 2019. For more information, see the Supplemental Materials.

Economic Modeling

The benefits and costs of leak management activities were estimated for each month of the project life (30 years), as illustrated in Fig. 1. The net present value was calculated by discounting future values according to
C(0)=C(t)(1+δ)−t
(1)
where δ is assumed to be 4% per annum. Accordingly, expected future values were calculated as
C(t)=C(0)(1+ω)t
(2)
where ω = the expected rate of growth in the cost. All equations used to estimate costs were adjusted to the present based on their year of publication using an average inflation rate of 2.5% per annum.
Fig. 1. Illustration (to facilitate visual interpretation, the figure is not to scale; generic units for time and cost) of a cash flow diagram for a leak management program with pressure reduction and leak surveys every four periods.

Pumps-as-Turbines

The costs of PATs and their associated generators were determined using empirical formulas developed by Novara et al. (2019) and methods used by Mitrovic et al. (2021). The cost of the PAT and generator is given as
Cp+g=β1QBEPHBEP
(3)
where β1 = an empirically determined coefficient (11,913.91); and QBEP (m3 s−1) and HBEP (m) are the best efficiency point (BEP) flow and head loss through the PAT. Other installation costs (OIC) are given by
Cp+g,OIC=(1−γ)γCp+g
(4)
where γ (0.26) = the fraction of the total installation cost represented by Cp+g. Following Mitrovic et al. (2021), we assume that the operations and maintenance costs of PATs and their generators are 15% annually of their total installation costs (Cp+g+Cp+g,OIC), with an annual growth rate (ωom) of 2.5% per annum.

Pressure Reducing Valves

The costs associated with PRVs include the capital cost of the valve itself, two gate valves, a strainer, and an air valve (Jones and Barkdoll 2022). The cost of PRVs and associated materials depends on the diameter of the valve, as given by
CPRV=β2eβ3D⏞PRV+β4eβ5D⏞Gas Valve+(β6D−β7)⏞Strainer+(β8D−β9)⏞Air Valve
(5)
where D (cm) = the diameter of the valve; and β2 (1,474.8), β3 (0.0824), β4 (500), β5 (0.0658), β6 (100.5), β7 (300), β8 (412.2), and β9 (512) are empirically determined coefficients (Jones and Barkdoll 2022). The operations and maintenance costs for PRVs were assumed to be negligible over the lifetime of the project.

Survey and Repair Costs

The initial survey and repair costs assume that all leaks are repaired, reducing the unreported leakage rate to zero or the unavoidable annual real losses level. The cost of the initial survey and repair is given by
Csu,i=(L0LavgF)+D
(6)
where L0 = the initial leakage; Lavg = the average leak flow rate; F = the adjusted leak repair cost; D = the full leak detection survey cost; and the initial leakage is assumed to be equivalent to Marin’s 2022 real losses (55,506.6  m3; 1,045 acre-ft), as reported to the California Department of Water Resources [the data are available through the Water Use Efficiency Data Portal (WUEdata - Public Portal, n.d.)]. The rate of growth of the costs (ωF and ωD) are assumed to be 2.5% per annum. The cost of surveying and repairing leaks after the initial survey and repair efforts is estimated as
Csu(s)=(R·sLavgF)+D
(7)
where s = the number of time periods (months) between surveys; and R = the rate of rise of unreported leaks. For more details, see the Supplemental Materials and Rupiper et al. (2022).

Water Lost

The volume of water lost during each month is calculated by integrating the leakage rate over time, as shown in Fig. 2, and given by
VL(t)=∫t−1tγRtdt
(8)
where γ = the fraction of the leakage rate that remains after pressure reduction (see Fig. 2) and is defined following the leak model used by Rupiper et al. (2022) as
γ=(P1P0)N1
(9)
where P0 = the initial service pressure; P1 = the new service pressure after an intervention; and N1 = the pressure-leakage relationship exponent given by
N1=1.5−(1−23×ICFILI)Frigid
(10)
where ICF = the infrastructure condition factor; ILI = the infrastructure leakage index; and Frigid = the fraction of pipes in the network that are constructed of rigid materials [here assumed to be 0.75 following Rupiper et al. (2022) in absence of the data required to make a more accurate assumption]. The pressures are estimated by the hydraulic model for the junctions or the nearest service connection. For more details, see the Supplemental Materials in Rupiper et al. (2022). Note that the function describing the actual leakage rate over time is a piecewise function (see Fig. 2) since the leakage rate is reset to zero (or the level of unavoidable losses) whenever a survey and repair activity takes place. The amount of water lost was calculated individually for each month. The cost of water is given by the variable production cost (Cvp), which is specific to each utility. To estimate the value of the lost water (CWL), we assume an annual growth rate for the variable production cost (ωvp) of 2.5% per annum.
Fig. 2. Illustration (generic units for time and leak rate) of the avoided leakage in a water distribution network after applying a leak reduction program consisting of leak detection and repair and pressure reduction.

Energy Produced

The amount of energy produced by a PAT (EPAT) is an output of the hydraulic model and is estimated using the relationship
EPAT=QHρgη
(11)
where Q (m3 s−1) = the flow; H (m) = the head loss; ρ (kg m−3) = the density of water; g (m s−2) = gravitational acceleration; and η (0.76) = the PAT efficiency (which may be slightly lower than what is possible) (Giosio et al. 2015). To estimate the value of the energy recovered (BER), we assume an average energy sale price of $0.12 per kWh and a cost growth rate (ωE) of 2.5% per annum. The estimated weekly energy production for the summer and winter models was averaged and used to determine the average expected monthly energy production.

Avoided Leakage

The volume of avoided leakage is here defined as the difference between the water that would have been lost if no leak management activities had taken place after the first survey and repair activities (illustrated by the top line in Fig. 2) and the amount of water actually lost given the proposed leak reduction activities (illustrated by the bottom piecewise function in Fig. 2). The value of the avoided leakage (BAL) each month is determined using the same methods given here for lost water.

Optimization Algorithm

With the goal of maximizing the net economic benefits over the study period, the optimization algorithm generates new hydraulic models by placing PRVs and PATs and disconnecting pipes where appropriate to create new DMAs. The creation of new DMAs allows the optimization to isolate service areas with higher than necessary pressure to facilitate pressure reductions while maintaining minimum customer service pressures. The optimization was performed under summer conditions and subsequently applied to the winter model to obtain results for both seasons. We utilize the multithreaded simulation optimization platform programmed in C++ in Linz et al. (2020) to evaluate the model with a particle swarm optimization algorithm (Kennedy and Eberhart 1995). Particle swarm optimization is a population-based search algorithm, which explores an optimization’s domain with a set of moving policies that gravitate toward local and global optima simultaneously. This strategy allows for the resilient exploration of a solution space when faced with many local optima, such as in the domain of hydraulic model optimization. The platform developed in Linz et al. (2020) is utilized to schedule, manage, and progress the optimization logic across iterations, while utilizing any programmable, generalized objective function.
Each particle in the particle swarm optimization algorithm consists of a policy vector (p^), which we define as a set of values that indicate the changes to be made within the model. The values refer to a set of indexed pipes, pumps, or valves [p∈(1…P)], which are sorted geographically along a 2D Hilbert curve, such that small changes to a pipe index p results in small changes to the geographic location of the installed PAT or PRV (Hamilton and Rau-Chaplin 2007). To make the optimization problem solvable with limited computational resources, the number of items in p^ was limited to four, which corresponds to the maximum number of PRVs or PATs that may be added to the system. For example, the policy might be p^=⟨p1,p2,p3,p4⟩=⟨3,6,9,11⟩, which would indicate that the optimization would attempt to place PRVs and PATs at pipes 3, 6, 9, and 11. The optimization always compares the economic viability of PRVs and PATs and selects the more advantageous option for each pipe. The algorithm may also choose to place fewer than four devices. Based on the model simulation (Sim(·)), the relevant hydraulic quantities can be modeled as deterministic functions of the specific asset p, the overall policy vector p^, and the selected timestep t. Observable hydraulic outputs (e.g., energy, head loss, or flow) for a specific asset p are given by
α(t)=Simα(p,p^,t)
(12)
where t−1 to t is the time period over which the simulation occurs. Several components of the net benefits formula can be evaluated from the hydraulic model as
CPE(p^)=∑t=1T∑p=1PCEnergy[{SimE(p,p^,t),p is pump0,otherwise](1+δ)−t
(13)
and
BER(p^)=∑t=1T∑p=1PCEnergySimE(p,p^,t)(1+δ)−t
(14)
where CPE(p^) = the total energy cost of the pumps in the network, which may change with the introduction of new infrastructure; SimE(p,p^,t) = the energy demand of p with the changes identified within p^ from t−1 to t; BER(p^) = the value of the net energy recovered by the PATs installed in the distribution system given the set of changes indicated by p^; and T = the duration of the study period.
A fundamental requirement of operating water systems is to supply adequate water pressure to customers (typically, at least 275.8 kPa or 40 psi), prevent suction pressures within distribution pipes, and prevent water tanks from draining excessively. Thus, the optimization problem is defined as
maxp^[BN(p^)]=maxp^[BAL(p^)+BER(p^)−CWL(p^)−Csu(p^)−Csu,i(p^)−Cp+g(p^)−Cp+g,OIC(p^)−CPE(p^,t)−CPRV(p^)]
(15)
where BAL = the value of the avoided leakage; BER = the value of the energy recovered; CWL = the value of the water lost to leaks; Csu = the cost of surveying and repairing leaks; Csu,i = the cost of the initial survey and repair activity; Cp+g = the cost of installing PATs and their associated generators; Cp+g,OIC = the operations and maintenance cost for PATs and generators; CPE = the value of the energy required to operate all pumps throughout the distribution system; and CPRV = the cost of installing pressure reducing valves. The optimization is subject to the constraints
min(SimCP(p^,T))>275.8  kPa
min(SimNP(p^,T))>0  kPa
and
min(SimTL(p^,T))>0  m
where SimCP(p^,T) = all customer pressures; SimNP(p^,T) = all nodal pressures; and SimTL(p^,T) = all tank levels. The pressure and tank level constraints are implemented as per-node or per-tank penalties that negatively impact the objective function with extremely large values for each constraint violation. Before the hydraulic simulation can be performed, each input vector p^ is used to generate a new hydraulic model with new PATs or PRVs and potentially with pipe closures. The construction of a new model consists of several steps, including the following:
1.
Evaluate the full hydraulic simulation for the original network.
2.
Determine the DMAs for the original network.
3.
For each potential PAT or PRV location p in p^:
a.
Replace the previous link p with the new PAT or PRV in the model.
b.
Align the new PRV or PAT with the average flow direction of the original link p.
c.
Set the PRV or PAT target downstream pressure to the average pressure of the node immediately downstream of the original link p.
4.
For each new PAT or PRV location p in p^:
a.
Try to find the shortest possible path connecting the upstream node to the downstream node for p within link p’s current DMA, which does not utilize link p.
(1)
If found, close the link in the middle of that path. Repeat this loop analysis until no path is found within the DMA that loops around the new PAT or PRV.
5.
Evaluate the DMAs for the new network.
a.
If any DMA is infeasible due to impossible network configurations or poor engineering practices, such as pumps looping on themselves or the lack of a water supply for storage tanks, then the decision vector p^ is rejected early with a poor performance value.
6.
For each new PAT or PRV location p in p^:
a.
Identify the minimum customer pressure (Pc) and node pressure (Pn) within the downstream DMA from the new link at p.
(1)
If found, reduce the setting for the new PAT or PRV downstream pressure target until Pc or Pn would violate an optimization constraint [e.g., 275.8 kPa (40 psi) customer service pressure, empty tanks, or vacuum pressure].
7.
Evaluate the full hydraulic simulation for the new network.
The particle swarm optimization algorithm was implemented with 500 particles and limited to 1,000 iterations based on an initial fitting exercise. At the conclusion of each particle evaluation, the decision on whether to place a PAT or PRV for each location p∈p^ is based on the maximized net benefit, as determined in Eq. (15). Each dimension of the vector p^ represents a single potential installation site, and, due to the regional sorting with the Hilbert curve, small changes to the decision vector would result in only small changes to the objective function. Overall, this strategy was selected to reduce dimensionality to exactly the number of PATs or PRVs being placed simultaneously and to maximize the search potential of the particle swarm optimization algorithm and ensure it adequately explores the decision space. If no improvement in the objective function is observed in 100 iterations, the optimization terminates. The algorithm typically produces several new hydraulic pressure zones that are served by one to two PATs or PRVs, with pipe closures as necessary (see Fig. 3). The procedures described here were also performed using a genetic algorithm (GA) based on the approach described in Linz et al. (2020) but modified to include Newton’s method.
Fig. 3. Example network subdivision performed on the southeastern section of the “Net3” hydraulic model: (a) prior to subdivision and placement of a new PRV or PAT, the section of the model was interconnected with the rest of the system and several storage tanks; and (b) following subdivision, a single valve was installed, a single pipe was disconnected, and approximately 124.1 kPa (18 psi) of excess pressure was removed such that a critical node received the target average pressure of 275.8 (40 psi).

Results

The particle swarm optimization resulted in the placement of four new PATs, the replacement of a throttle control valve with a PAT, a total water savings of 8,706,447  m3 (2.3×109  gal.), average power production of 1.5 to 2.9 kW, and net economic benefits of $1.9×106 over the 30-year study period. The particle swarm optimization algorithm terminated after 100 iterations without improvement before reaching the 1,000-iteration limit. As shown by the results in Table 1, all DMAs except one were suitable for PAT placement and leak reduction activities with positive net economic benefits. Four new DMAs were created during the optimization to maximize the potential benefits of pressure reduction strategies. Figs. 4 and 5 illustrate the estimated pressure changes throughout the distribution network resulting from the optimization. Considering all nodes during the summer and winter extended period simulations, the average pressure throughout the distribution system was reduced by 6.4% after optimizing. Fig. 6 shows the water demand, energy demand, and production for each DMA. The genetic algorithm optimization resulted in a different, but less optimal, distribution system configuration.
Table 1. Summary of the particle swarm optimization results (if the values are different under summer and winter conditions, a range is given)
DMAaAverage demand (m3 d−1)PRVbPATcNodesdPipe length (m)Average power demand (kW)Average power produced (kW)Survey interval (y)Avoided leakage (m3×10−3 per 30 y)eNet benefits ($×10−3 per 30 y)
1f,g0.4–0.6002161.6–3.20.0———
2h,i127.9–221.301552,4670.00.3–0.62.2–2.8264.2–269.255.5–56.1
30.6–3.50011510.00.05.12.50.2
4429.0–770.6001497,3643.6–6.60.01.61,012.8–1,014.2214.1–214.4
5110.0–201.700493,0802.0–3.70.02.2325.5–328.166.6–67.3
6j4.9–6.3001966.2–10.10.015.10.90.2
712.0–30.10094740.1–0.30.02.829.2–29.45.3–5.4
870.5–114.900311,7320.6–0.90.02.8162.1–163.132.6–32.9
974.9–137.100221,2140.8–1.50.02.2128.2–129.326.2–26.5
10f6.0–11.002k,l31150.00.2–0.510.15.41.4
11f219.6–380.401k833,4200.00.3–0.52.8412.4–413.993.3–93.5
12f,i626.6–1,111.61m1k24011,6410.00.7–1.31.61,993.5–2,000.6441.3–443.3
1317.2–29.82m0180.00.02.80.60.1
14d0.0–0.02m0050.00.02.80.40.1

Note: Valves and pumps are considered as belonging to a DMA only if they are upstream.

a
District metered area.
b
Pressure reducing valve.
c
Pump-as-turbine.
d
Customer nodes.
e
For example, 2,500×10−3=2.5.
f
Created during optimization.
g
No beneficial leak detection and repair strategy were identified.
h
Pipe length reduced by 1.7% during optimization.
i
Winter avoided leakage is higher than summer; the opposite is true for all others.
j
Pipe length reduced by 99.4% during optimization.
k
Placed by optimization.
l
One PAT replaced a throttle control valve.
m
Preexisting.
Fig. 4. Plot of the empirical cumulative distribution function for customer pressures before and after particle swarm optimization (summer and winter data are combined).
Fig. 5. Optimization results (particle swarm) for the calibrated summer period model. White regions represent areas with lower-than-average pressure; dark regions represent areas with higher-than-average pressure. Regionality of pressure did not change after optimization, though the magnitudes of pressure did change in select regions. (a) Average pressure prior to optimization and placement of new PRVs or ERTs; and (b) changes in average pressure following optimization (some regions actually increased in pressure, but these areas are so small that they are not visible on the map shown here).
Fig. 6. (a) Total hourly water demand for the distribution system; the band shows the minimum and maximum values; and (b and c) total hourly energy demand and production for the distribution system. Day 0 starts at 00:00.

Discussion

The particle swarm optimization successfully reduced pressures throughout the distribution network. As shown in Fig. 4, pressure reductions occur mainly between 275.8 to 896.3 kPa (40 to 130 psi). Pressures below 275.8 kPa (40 psi) were not significantly reduced due to minimum customer pressure requirements, while pressures above 896.3 kPa (130 psi) are likely associated with too little flow to make energy recovery and pressure reduction economically feasible. Fig. 5 shows the spatial distribution of pressure reductions and indicates that reductions of average pressure as high as 137.9 kPa (20 psi) occur in a significant portion of the distribution network. Although some areas of the network increased in pressure, the heatmap shown in Fig. 5 considers only pressure reductions because areas where pressures increased are so small, they cannot be seen. The lowest pressures observed in the distribution network likely belong to junctions located near tanks, which tend to occur at higher elevations and feed into DMAs without assistance from pumps, leading to lower pressures for customers immediately adjacent to the tanks. For this reason, customers are typically either not connected to DMAs with tanks at their elevation or pumps are used to lift water stored in tanks to the target hydraulic grade lines. High pressures within the distribution network are mostly along the coastline and are associated with significant elevation change within the DMA. Pressure reductions were the result of the placement of five PATs and the creation of four new DMAs to restrict flow and isolate high-pressure areas. Of the five preexisting PRVs, none were converted to PATs (due to modeling constraints, PRVs could not be removed). It appears that, in locations where additional pressure management was feasible, PATs were more economically viable than PRVs. As shown in Table 1, the total estimated energy recovery by PATs is equivalent to 10% to 11% of the current energy requirements (i.e., energy required for pumping). As shown in Fig. 6, peak energy recovery generally aligns with peak water demand. The additional energy required to pump water lost to leaks if no leak management activities were implemented is not included here, though it would likely be significant over the 30-year study period.
The particle swarm optimization also successfully identified the optimal leak survey intervals for 13 out of the 14 DMAs, ranging from 1.6 to 15.1 years between survey and repair activities. Performing the analysis at the DMA level allows for greater precision in targeting areas where fixing leaks is more valuable. Survey and repair activities in combination with pressure reduction are estimated to prevent a significant amount of leakage over the study period, equivalent to 13% to 23% of current customer demand. This does not mean that customer demand would be reduced by 13% to 23%. Rather, this is the equivalent amount of water that would be lost if leak management activities were not implemented over the study period. This value does not include the benefits of the initial surveys and repairs over the study period, as shown in Fig. 2, and is thus a more conservative estimate. Because the hydraulic model used for this analysis is demand (as opposed to pressure) driven, determining reductions in customer demand due to interventions is not feasible.
Leak detection and repair, pressure management, and energy recovery are generally considered independently in leak management programs and optimizations found in the literature. However, because implementing either strategy alters the hydraulic characteristics of a distribution system, they are interdependent and should be optimized together. Although doing so is more challenging, the results are more realistic and useful for water utilities. This analysis demonstrates the feasibility of considering both approaches simultaneously using hydraulic modeling and economics and provides a case study for water utilities considering a similar approach. However, these results are sensitive to model assumptions, and more rigorous quantification of model inputs (e.g., survey and repair costs) is recommended when applying this methodology in practice. This may require increased data collection efforts by water utilities to better understand relevant system characteristics (e.g., the rate of rise of leaks). Additionally, because the results are only as reliable as the hydraulic model on which the analysis is based, only calibrated and proven models should be used.
Although the particle swarm optimization provided a positive result and measures were taken to increase confidence in the solution, as with all heuristic optimization algorithms applied to complex problems, we cannot be certain that the global optimum was found. Other optimization algorithms may recommend alternative distribution system configurations due to differences in how they navigate the solution space. For example, the genetic algorithm optimization approach discussed previously yielded a significantly different solution than the particle swarm optimization. However, the alternative solution is estimated to recover less energy and results in a less desirable distribution of customer pressures. We do not claim that particle swarm optimization is the best possible approach in all scenarios but instead provide a general framework for practitioners and an example optimization algorithm that appears produce reasonable results. Practitioners should carefully consider the optimization algorithm they choose to implement. Future research and improvements to this methodology could include considering the reliability of the water supply, carbon emissions, alternative conservation values, time-of-use electricity rates, the relocation of existing pressure management devices, and the administrative costs of implementing the leak management program activities (Rupiper et al. 2022).

Supplemental Materials

File (supplemental materials_jwrmd5.wreng-6428_hammond.pdf)

Data Availability Statement

Some or all data, models, or code used during the study were provided by a third party. Direct requests for these materials may be made to the provider as indicated in Acknowledgments. These materials include ArcGIS files representing Marin’s water distribution system as well as pressure, flow, pump and valve operation, and tank level data. The data that support the findings of this study were used under a nondisclosure agreement and so are not publicly available. The underlying code for this study is publicly available on GitHub in two public repositories: https://github.com/ucd-cwee/UCD_WaterWatch; and https://github.com/ucd-cwee/LeakOptimization.

Acknowledgments

This study was supported through a Demonstration of Energy and Efficiency Developments (DEED) grant provided by the American Public Power Association through the California Municipal Utility Association under Grant CG-2311. Additional support was provided by Marin Municipal Water District under Agreement MA-5910. Any opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily reflect the views or opinions of the funding agencies.

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Information & Authors

Information

Published In

Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 150 • Issue 8 • August 2024

Copyright

This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.

History

Received: Oct 5, 2023
Accepted: Feb 28, 2024
Published online: Jun 3, 2024
Published in print: Aug 1, 2024
Discussion open until: Nov 3, 2024

ASCE Technical Topics:

  1. Business management
  2. Case studies
  3. Economic factors
  4. Energy engineering
  5. Energy infrastructure
  6. Energy recovery
  7. Energy sources (by type)
  8. Engineering fundamentals
  9. Hydro power
  10. Infrastructure
  11. Lifeline systems
  12. Management methods
  13. Methodology (by type)
  14. Pipeline systems
  15. Pipes
  16. Practice and Profession
  17. Pressure distribution
  18. Pressure pipes
  19. Renewable energy
  20. Research methods (by type)
  21. Water and water resources
  22. Water leakage and water loss
  23. Water management

Authors

Affiliations

Charles Hammond [email protected]
Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Univ. of California Davis, One Shields Ave., Davis, CA 95616. Email: [email protected]
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Robert Good [email protected]
Research Engineer, Center for Water Energy Efficiency, 215 Sage St. Suite 200, Davis, CA 95616. Email: [email protected]
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Frank Loge https://orcid.org/0000-0002-8264-7021 [email protected]
Professor, Dept. of Civil and Environmental Engineering, Univ. of California Davis, One Shields Ave., Davis, CA 95616 (corresponding author). ORCID: https://orcid.org/0000-0002-8264-7021. Email: [email protected]
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