Viability of Pressure-Reducing Valves for Leak Reduction in Water Distribution Systems

Since water distribution systems are so important to public health and many are leaking in unknown locations, a modeling study was performed to investigate the feasibility of installing pressure-reducing valves (PRVs) in various locations throughout several systems. A PRV was tried in each pipe, one by one, and the total cost (energy costs plus opportunity costs of losing water that could have been sold) was calculated. It was found that installing a PRV in the upstream pipes reduced costs the most and that putting a PRV in some pipes actually lost money due to the high cost of the PRV and associated fittings. Also, a PRV on the upstream portion of a large branch saved water leakage. Energy is saved when a PRV is placed near a pump for systems with high energy consumption.


Sustainability
There are 17 sustainability goals identified by the United Nations that are aimed at transforming many aspects of the world [1]. Of interest here are the goals pertaining to water distribution systems (WDSs), such as precipitation that controls lake and aquifer levels, water supply, and energy consumption of pumps. These goals are stated as follows: Goal 3, "Good Health and Well-Being" are important because drinking water aids in health; Goal 6, "Clean Water and Sanitation" are for the same reason; and Goal 11, "Sustainable Cities and Communities" are important because reduced pumping and energy consumption relating to the quantity of pollution produced for electricity generation. This is important since WDSs use pumping, which runs off electricity that adds to greenhouse gas emission.

Water Distribution Systems
Water distribution systems (WDSs) use groundwater and surface water to supply users with the required amount of water. They consist of reservoir(s), pipes, and a storage tank(s) [2]. Users consume water in a diurnally varying demand pattern. Most reservoirs are lower in elevation than the users, thereby necessitating pumps to convey water [3]. These pumps are powered with electricity that primarily is generated through the burning of coal, thereby emitting greenhouse gases [4]. Many factors that can affect energy consumption include pipe diameter [5] and elevation, pump location and horsepower, and storage tank location and water levels [6][7][8], among others.

Leaks
According to the EPA, water distribution systems (WDS) in the USA lose an average of 14% of their water through leaking, with some water losses in WDSs reaching over 60% [9]. Water losses due to leakage can be due to a variety of reasons, such as aging infrastructure, poor management, or inadequate design or construction [10]. Losing water due to leakage has economic consequences, because money is spent on treating and pumping any water that leaks out of a WDS. Since consumers are not charged for water that leaks out of a WDS, this money that is invested into leaking water is totally lost. The operational management of pumping schedules considering the leakage rates can be counter-intuitive with filling of the tanks in the day being suggested [11]. Leaks cause additional flow in pipes and, therefore, cause additional pumping costs [12,13]. Repairing the leaks will reduce the pumping costs [14]. WDSs can be designed to minimize background leakage as well [15].
Due to the increased leakage at higher pressure, pressure management is one of the most crucial tools in reducing leakage in WDS [16]. This allows pressure-reducing valves (PRVs) to be effective in reducing water losses to leaking in WDSs [17,18]. However, using a PRV to reduce water losses due to leaks can have a relatively expensive initial cost [19]. Leaks may also be able to be reduced with flexible storage tanks [20].
Not only that, but all of the hydraulic factors must also be carefully considered to determine an acceptable location. Even if it is determined that a PRV can reduce leakage, it is difficult to say if the recovered losses will make up for the upfront cost of the PRV. This makes the decision to implement a PRV and where to put one very difficult for WDS managers interested in minimizing water losses due to leaks.
Hydraulic modeling is an essential tool in assessing and solving problems related to WDSs. Hydraulic modeling software can be used to evaluate issues and make decisions relating to water quality, leaking, hydraulic inadequacy, WDS expansion, and many others [17]. EPANET is a hydraulic modeling software that is commonly used to tackle problems and make decisions in WDSs and is the hydraulic modeling software used in this study [43].
Creaco has performed some valuable studies on the economics of leakage reduction in WDSs using PRVs and also RTCs (real-time controlled valves). In Ceaco and Pezzinga [44], multi-objective optimization of pipe replacements and control valve installations for leakage attenuation was examined. This study differed from the present one in that pipe replacements as well as conventional valve (not PRVs) location and settings were considered. A tradeoff was found between the cost of valve installation and pipe removal with water lost due to leakage. In Creato and Haider [45], leaks were reduced by multi-objective optimization of control valve installation and district-metered area (DMA) creation. New algorithms were used and found to be an improvement. This differs from the present study in that complete enumeration is used here, a method which tries every possible possibility and not just a subset thereof. Again, a tradeoff was discovered between cost and leakage water loss. Creaco and Walski [46] investigated the economics of leakage reduction through PRVs and RTCs. It was also found that a tradeoff exists. This study did not include opportunity costs, however, as the present study does. Opportunity costs are the cost of the lost water. The customer could have been charged for this water and, therefore, lost money. Creaco and Walski [47] studied the economics of RTCs for leakage reduction, while the present study only studied PRVs. All these studies, as well as the present one, calculated lifecycle costs and, therefore, are more complete than simply considering the initial costs. In addition, Zhang et al. [48] studied the optimal location of DMAs and PRVs and found that this combination can reduce leakage but focused more on the calculation method rather than the leakage reduction amounts. Their algorithm was demonstrated on a single medium-sized system.

Study Objectives
Since no studies have investigated the optimal location of a PRV to minimize the payback period and lifecycle costs (including opportunity costs of lost water revenue and energy pumping costs), this study uses network modeling to accomplish this.

Description of Existing Water Distribution Systems Modeled
Seven real water distribution systems were modeled for this investigation, using the hydraulic modeling software EPANET. Of the seven models used, six of them are based upon realworld municipal water distribution systems with data provided by their water managers. The remaining system is a simple, hypothetical system provided by EPANET. The seven systems tested vary in terms of size (Table 1). Sizes ranged from 8 to 135 pipes, 6 to 118 junctions, and 1 to 2 reservoirs. The system models also vary in terms of type and complexity. For example, System 2 is a system made up completely of branches, while the system is made completely of loops, and the remainder of the systems are made up of both branches and loops. The one constant in all of the systems is that all systems modeled contain at least one pump and one reservoir.
All systems had pump characteristic and efficiency curves, a demand pattern at each junction, an energy price curve, and a price of water included before, and PRVs were installed in the modeling effort ( Fig. 1).

Including Leakage in Network Models
A leakage rate of 14% was used in every model, which is considered to be the average water distribution system leak rate in the USA [9]. A single leak size was used for simplicity, since the number of combinations and permutations of leak sizes at all system junctions is prohibitively large. It was assumed that leaking was a part of the base demand, since the models are based on real-world water demand data. Leaking is represented in EPANET in the form of an emitter applied at junctions. To more accurately model leaking in the water distribution systems, 14% of the base demand was removed from each junction, and that demand was then replaced in the form of an emitter. The behavior of an emitter in EPANET can be predicted using Eq. (1) [42].
where q is the flow rate of the leak, p is the pressure at the location of the leak, C is the emitter coefficient, and N is the pressure exponent.
Using a method provided by Cobacho et al. [49], this equation was repurposed to calculate an emitter coefficient for every junction that will result in the desired leakage rate of 14% (Eq. (2)).
where q net,real is the total leaking demand of the existing water distribution system (assumed to be 14% of the total demand), p net is the average pressure of the entire distribution system over the course of a 6-day simulation, and j is the total number of junctions in which emitters are to be applied. For each water distribution network modeled, a different emitter coefficient was computed using the method described. In addition, 14% of the base demand at every junction was then removed, and the computed emitter coefficient was then applied at every junction to replace the 14% demand removed. Six-day simulations were then run on each system to ensure that the demand of the system was equal to the original value, and the emitter coefficient was calibrated accordingly. It is worth noting that in real water distribution systems, there are many factors that dictate where leaks are more common and how much they may be leaking. This could include the age of the pipes in different locations, the soil type around the pipes, or the specific methods used when installing the pipes of the water distribution system. These factors are impossible to consider due to the limited knowledge of the history and conditions of the networks modeled. It is for this reason that the same-sized leak at every junction in the water distribution system models was used, and assumptions were not made about where leaks may be more likely to occur.

Modeling Pressure-Reducing Valve Locations
In order to limit water loss due to leakage, pressure-reducing valves can be used to lower unnecessarily high pressures in a water distribution system where leaks exist. In EPANET, pressure-reducing valves will limit the pressure at a point in the pipe network. A PRV will be partially opened to achieve the pressure setting downstream of the valve if the pressure upstream of the valve exceeds the PRV setting. Otherwise, the valve will be fully open if the upstream pressure is below the PRV setting or completely closed if the downstream Table 1 Characteristics of WDSs used P-T state, pump-tank state; N, pump is near the tank; M, tank is in the middle of the system; F, pump is far from the tank; D, water is pumped directly to the tank and not into the system; S, water is pumped directly to the system from which it goes into the tank * Booster pump pressure is above the upstream pressure. Pressure-reducing valves are not allowed to be connected directly to another pressure-reducing valve, a tank, or a reservoir in EPANET [43]. In order to test the impacts of a pressure-reducing valve in a water distribution system, a MATLAB program was developed in the MATLAB toolkit for EPANET. The MAT-LAB program starts by selecting any given pipe in the water distribution system where a PRV can be placed. This pipe is then removed from the system and replaced with a pressurereducing valve of a matching diameter and an initial setting of 19 psi. A 6-day simulation was then run and checked to ensure that the minimum pressure in the entire WDS model over the entire simulation duration does not drop below 20 psi, thereby ensuring a pressure above 20 psi, as it should be during normal operating conditions. The MATLAB program also ensured that the tanks in the WDS model were filling and draining properly. The PRV setting was then raised 1 psi at a time until the pressure and tank requirements were met. If the system failed to meet the requirements with a PRV no matter how large the setting was, it was considered to be a non-viable PRV location. After the pressure and tank requirements were met, a final simulation was run with the minimum pressurereducing valve setting for that specific valve to collect data. In Fig. 1 Example of user demand pattern (a), pump characteristic (b), pump efficiency (c), and energy tariff (d) curves from System 1. Similar curves are used in all seven systems with appropriate values included the final simulation, the pipe name, pressure-reducing valve setting, total system water demand, and daily energy cost were recorded. The MATLAB program then removed the PRV from the system, and the original pipe was then placed back to its original value. This process was then repeated for every possible pressure-reducing valve location in all of the 7 WDS models used.
A single PRV was modeled to represent a management budget sufficient to buy only one PRV. If additional funds were available, then a second PRV could be added. After the installation of the first PRV, pipe flows could change, thereby making the second-ranked optimal site potentially different from that shown here. Also, adding a second PRV may alter the optimal setting of the first PRV.

Cost of Installing a Pressure-Reducing Valve
In order to properly compute a PRV's net present value (NPV) and payback period (PP), several factors surrounding the installation of the PRV had to be considered. Installing a PRV requires the use of two gate valves, a strainer, and an air valve [43]. The price of these components was considered on top of the price of a PRV and the cost of designing, installing, and maintaining the PRV as a part of the system. The sizes of the PRVs, gate valves, and strainers were assumed to be the same as the pipe in which they would be installed. In order to determine the air valve size required, the procedure outlined on Flomatic Valves' website was utilized in the MATLAB program [51]. Prices for gate valves, strainers, air valves, and PRV's with their associated sizes were also obtained from Flomatic Valves' website [19]. However, the prices obtained did not include every size of hydraulic components that exist in all of the water distribution systems. It is for that reason that equations were developed for the relationship between PRV, gate valve, and strainer size with their associated cost. Equations (3), (4), (5), and (6) are the equations used to compute PRV, gate valve, strainer, and air valve cost based on size based on information from Flomatic.
It can then be assumed that the cost of designing, installing, and maintaining the PRV is an additional 15% of the cost of the total cost of the PRV, two gate valves, strainer, and air valve [43].
where the C values represent the total cost of the valve in question, and D represents the diameter of the valve to be used.

Calculating Pressure-Reducing Valve Net Present Value and Payback Period
To determine the practicality of putting a PRV in a municipal WDS in order to save money, the NPV and payback period of a PRV for its associated location were calculated using Eq. (7).
where TC represents the cost of the PRV, C prv ; gate valves, C gv ; strainer, C s ; and air valve, C av , as well as the associated design, installation, and maintenance cost. CS t represents the difference in yearly cost due to changes in water demand and energy demand as a result of the PRV. The time in years is represented with t, L represents the lifetime of the pressure-reducing valve, and r represents the rate of inflation. A 15-year NPV time for the PRV [50] and an inflation rate of 0.02 were both assumed. In order to determine the payback period of the PRV, the time in which the NPV of the PRV is equal to 0 had to be calculated. This was accomplished by setting the NPV in Eq. (7) equal to 0 and then solving Eq. (7) for t. Payback periods that exceeded 50 years were labeled to "never" pay for themselves. This was considered to be the lifespan of a WDS, and a payback period of anything longer would likely render the investment to not be recovered.

System 1
Of the seven PRV locations tested in System 1 (Fig. 2), four of the pipes paid for themselves within 15 years of being installed, with the highest NPV being $112,346.78 if installed in Pipe 5. Two of the PRV locations had negative 15-year NPVs, and they never paid for themselves within 50 years. The remaining possible PRV location is considered to not be viable, because when a PRV was placed here the tank and pressure requirements could not be met. In the Supplemental Information are the names of the pipes replaced with PRVs, the associated PRV setting, associated daily water cost changes, associated daily energy cost changes, associated 15-year net present value, and associated payback periods for System 1.

System 2
Of the 113 PRV locations tested in System 2 ( Fig. 3), all of the PRVs had negative 15-year NPVs, and none of the PRVs were able to pay for themselves within the 50-year lifetime. While all but two of the PRVs were able to save some amount of water, this was not enough to overcome all of the costs associated with implementing a PRV. In the Supplemental Information are the names of the pipes replaced with PRVs, the associated PRV setting, associated daily water cost changes, associated daily energy cost changes, associated 15-year net present value, and associated payback period for System 2 ordered by water saved.

System 3
Four of the PRV locations tested in System 3 ( Fig. 4) had positive NPVs out of the 38 locations tested, with the highest 15-year NPV being $199,795.19. These three PRV locations were all located directly upstream of the only pump in the system, and the majority of their contributions came in the form of energy savings. Of the remaining PRVs, four of them paid for themselves after 15 years and before 50 years, and the rest never paid for themselves in a reasonable amount of time. Twenty-six of the PRVs were able to save on daily water cost, and three PRVs had produced substantial energy savings. In the Supplemental Information are the names of the pipes replaced with PRVs, the associated PRV setting, associated daily water cost changes, associated daily energy cost changes, associated 15-year net present value, and associated payback period values for System 3.

System 4
Out of the 61 PRV locations tested, only one PRV in System 4 ( Fig. 5)

System 5
None of the PRVs tested in System 5 (Fig. 6) had a positive 15-year net present value; however, five of the PRV locations had payback periods of under 50 years ranging from 22 to 48 years. These five PRV locations are all on the same branch starting directly in front of the pump, and all five of these PRV locations are consecutively connected. The remaining 23 PRVs never paid for themselves in a reasonable amount of time. Every PRV tested in System 5 was able to save water, with water savings ranging from $0.06 to $1.00 per day. In the Supplemental Information are the names of the pipes replaced with PRVs, the associated PRV setting, associated daily water cost changes, associated daily energy cost changes, associated 15-year net present value, and associated payback period for System 5.

System 6
PRV locations were tested in System 6 ( Fig. 7), and none of these PRVs had positive 15-year NPVs. Two of the PRVs had payback periods of 33 and 38 years, while the remainder if the pipes did not pay for themselves in a reasonable amount of time. Thirty-one of the PRVs were able to contribute to water savings with daily water cost savings ranging from $0.02 to $0.54 per day. Nine of the top ten 15-year NPV PRV locations were all located on the same mainline of a branch that comes from the only tank in the system. In the Supplemental Information are the names of the pipes replaced with PRVs, the associated PRV setting, associated daily water cost changes, associated daily energy cost changes, associated 15-year net present value, and associated payback period for System 6.

System 7
In System 7 (Fig. 8), 125 PRV locations were tested. Eleven of the PRVs had positive 15-year NPVs ranging from $225.20 to $9,915.96. Twenty-three other PRVs had payback periods ranging from 31 to 16 years. The remainder of the PRVs did not pay for themselves in any reasonable amount of time, or the system could not meet pressure and tank requirements with the PRV. Presented in In the Supplemental Information are the names of the pipes replaced with PRVs, the associated PRV setting, associated daily water cost changes, associated daily energy cost changes, associated 15-year net present value, and associated payback period for System 7.

Water Savings with PRVs
Substantial water consumption changes were seen from placing PRVs in all systems. Water savings ranged from − 6017 to 37,232 L per day, where a positive volume means water savings. If you define a branch as a series of pipe connections in which all pipes downstream of the start of the branch lead to a dead end, then a strong relationship can be seen with placing a pressure-reducing valve in the mainline of a branch and saving water. For example, the following observations were made on water savings for the systems modeled. In System 2, the PRV location that saves the most water is in the 5th pipe (Pipe ID: "42") on the mainline in the largest branch of the system. In System 4, the PRV location that saves the most water is located in the first pipe (Pipe ID: "Pi60") of the largest branch in the system. The PRVs that were placed in the remaining 7 branch mainline locations (Pipe IDs: "Pi10," "Pi57," "Pi7," "Pi9," "Pi18," "Pi61," and "Pi56") of System 4 correspond the next 7 highest-ranking PRV locations in terms of water savings. In System 5, the PRV location that saves the most water (Pipe ID: "3") is located in the first pipe of the mainline of the largest branch in the system. The next 4 highest-ranking PRV locations in terms of water savings were all directly downstream of this pipe on the mainline. In System 6, the PRV location that saves the most water (Pipe ID: "22") is the 5th pipe in the mainline of the largest branch in the system. The other pipes that saved the most water in System 5 are located either directly before or after this pipe in the mainline of the largest branch. In System 7, the PRV location that saved the most water (Pipe ID: "P-530") is in the first pipe of one of the smaller branches in the system. While the pipes that saved the 2nd, 3rd, and 4th most water (Pipe IDs: "P-1100," "P-220," and "P-210") are the first 3 pipes in the mainline of the largest branch in System 7. A similar observation could not be made in Systems 1 and 3, because they had no dead ends in their pipe networks. Due to these observations, it can be concluded that by placing a properly set PRV in the mainline of a branch in a leaking WDS, you can potentially lower the rate of leakage in the WDS.

Energy Savings with PRVs
In Systems 2, 5, and 6, placing PRVs in them had little to no impact on energy cost, with changes in daily energy cost ranging from − $0.64 to $0.07 per day, where a positive cost is a saving. This is likely due to the low daily energy cost of these existing systems, and this makes for little room for change in terms of energy cost. However, placing PRVs in Systems 1, 3, 4, and 7, where daily energy cost was much higher, proved to have substantial impacts on daily energy depending on the location. In the case of Systems 1, 3, and 4, this meant substantial energy savings, with maximum changes in energy cost being $2.64 per day, $44.38 per day, and $3.56 per day, respectively. In the case of System 7, this meant substantial added daily energy cost, with the highest daily cost change being − $103.56 per day. Something all of these extreme cases share is that their respective PRV locations are all within very close proximity to the pumps in their respective systems. While added energy cost is expected from placing a PRV in close proximity to a pump due to adding head loss, the observation of substantial energy savings from placing a PRV in close proximity to a pump is counter-intuitive. One explanation for water savings explored was that by having to pump less water due to reduced leakage, the pump would potentially not have to work as hard. However, in many cases where energy savings were observed, very little water savings and even increases of leakage were observed along with it. The only remaining speculation is that PRVs in loops in close proximity to a pump impact the flow-rate of the pump in such a way that is more efficient. In other words, if the pump in the system was operating at a relatively high and inefficient flow-rate before a PRV was placed, placing a PRV in front of the pump in could cause the pump to operate at a lower flow-rate that is higher on the pump's efficiency curve. This could explain the energy savings observed from various PRV locations in Systems 1, 3, and 4. Conversely, if a pump were operating at a flow-rate that corresponds to peak efficiency, placing a PRV could cause the pump to operate at a less efficient flow-rate on its pump efficiency curve. This could potentially explain the increase in energy cost from various PRV locations in System 7. This idea is purely speculation and requires further investigation.

Money Savings with PRVs
Out of all of the 7 systems tested, a total of 20 PRVs were found to pay for themselves within 15 years of being installed, with 11 of these PRVs being in System 7, 4 of these PRVs being in System 1, 4 of these PRVs being in System 3, and one of these PRVs being in System 4. Systems 2, 5, and 6 never had a PRV pay for itself within 15 years. This is likely due to the fact that Systems 1, 3, 4, and 7 leak much more value in water each day than Systems 2, 5, and 6. Systems 1, 3, 4, and 7 leak $351.316, $3507.71, $153.98, and $205.294 in water value per day, respectively, while Systems 2, 5, and 6 leak only $1.469, $15.67, and $6.25 in water value per day. This pattern extends into daily energy cost as well. Systems that had higher daily energy cost had more potential to save higher dollar amounts on daily energy cost with a PRV. Due to this observation, it can be concluded that the potential for saving money in a WDS using a PRV is much more viable in a system with much higher demand and more leaking potential. It is also worth noting that this makes saving money with PRVs much more viable in places where the value of water is much higher.

Conclusions
Testing all possible PRV installation locations in seven water distribution system models resulted in the following conclusions: 1. By placing a properly set PRV in the mainline of a branch in a leaking WDS, you can potentially lower the rate of leakage by a substantial amount. 2. By placing a PRV in close proximity to a pump, the daily energy cost of pumping can change significantly, lower or higher, since the amount of leakage water loss can make up for the additional headloss from a PRV. 3. Saving money with a PRV becomes more practical as the rate of the price of water leaking goes up, as well as when the daily energy cost goes up. 4. Not all locations of PRVs result in recovered costs within the lifetime of the system. 5. Beyond cost, saving energy has implications for global climate change since the amount of energy usage is reduced.

Discussion
For the test done on placing PRVs in the 7 systems modeled, it was assumed that the lowest possible PRV pressure setting that could maintain system pressure and tank levels was the optimum pressure setting for saving money with a PRV. While this may be true in most cases, it is likely not true for all cases. Finding the optimum PRV settings to save money could be further investigated and could show that PRVs have even more potential to save money in WDSs. Additionally, in the simulations run, only one PRV was tested at a time in the WDSs. Placing multiple PRVs in WDS models at one time, especially at least one PRV in each pressure zone and in optimal places could be investigated to see if this increases the money saving potential of PRVs. It was noted in that PRVs seem to be more effective in systems that leak more. This study that used fixed-speed pumps with on-off controls based on tank levels. However, variable-speed pumps are another option, which also regulate pressure and, therefore, leakage attenuation. Although a variable-speed pump does not always save energy since a lower speed may lead to longer pumping times if the storage tank(s) cannot be filled as quickly.
It is possible that results would be slightly different if the emitter exponent was normalized by the length of pipe, rather than by the number of nodes, as was done here. This may make a difference if pipes were long and the number of nodes was few. The example of Cobacho et al. [42] was employed here.

Data availability
All data is included in Supplemental Information submitted with this article.