## Abstract

Applying pressure management reduces lost water and excessive hydraulic pressures in water distribution networks (WDNs). There are currently four different types of pressure management in the literature, i.e. fixed outlet, time modulated, flow modulated, and remote node modulated. The primary device used in pressure management is the pressure reducing valve (PRV) that dynamically controls the outlet pressure by moving up and down its main valve element. In this study, we firstly introduce the dynamic PRV model with four different pressure management types to the source code of EPANET v3.1 software and assess the effect of different valve opening schemes on pressure graphs and leakage quantities. The results showed that dynamic PRV significantly reduces lost water amounts and excessive hydraulic pressures in the WDN when valve opening is continuously adjusted. Our smart PM extension implemented into EPANET v3.1 software is publicly available in Zenodo repositories (https://zenodo.org/record/6243078).

## HIGHLIGHTS

The dynamic PRV model is introduced to EPANET 3.

Four different PM schemes are incorporated into EPANET 3.

The newly introduced EPANET 3 code is rigorously tested in the hydraulic model of two water distribution networks.

### Graphical Abstract

## INTRODUCTION

Providing high pressures in water distribution networks (WDN) to supply sufficient water to consumers, is essential for water utilities. So that the users’ water demand is satisfied and municipal duties are accomplished (Walski *et al.* 2007). On the other hand, excessive pressures in WDNs can cause numerous leakage-induced water losses, pipe fractures, and excrescent water consumption (Thornton *et al.* 2008). Especially at night, pressures increase due to the decreasing velocities, making WDN more fragile (Farley & Trow 2003). For this reason, managing pressure has a pivotal role in the reliability and resilience of WDN.

Commonly used four Pressure Management (PM) types are (1) Fixed Outlet (FO) PM, (2) Time Modulated (TM) PM, (3) Flow Modulated (FM) PM, and (4) Remote Node Modulated (RNM) PM (Hamilton & Mckenzie 2014; Vicente *et al.* 2016). The first one (i.e. FO PM) is the most preferred PM type (Vicente *et al.* 2016). In this management approach, a constant pressure level at any time is targeted in the main supply pipe of district meter areas (DMA) with no consideration of flow rate or time. The second approach (TM PM) comprises adjusting pressure according to time. As is known, pressures are high at night, contrary to daylight hours. In the TM type pressure management scheme, night-time high pressures are targeted to be lower values than those in the daytime as this helps to significantly reduce leakage risk (Awad *et al.* 2009). The FM type pressure management scheme ensures a pressure value for every single different flow rate entering the DMA. For that, a pressure-flow curve is used to generate sufficient pressures at the critical nodes (Abdelmeguid 2011). Finally, the fourth approach (RNM PM) aims to provide the minimum allowable pressure value at the critical node of the DMA (Creaco *et al.* 2019). Inlet pressure of DMA is updated consistently to satisfy restrictions about minimum allowable pressure in WDN (Koşucu *et al.* 2021). This method is also called real-time pressure control (Campisano *et al.* 2020).

The primary instrument of the PM is Pressure Reducing Valve (PRV) (Nicolini & Zovatto 2009). PRVs are installed on supply pipes of DMAs and reduce excessive pressures to manage pressure properly (Ulanicki *et al.* 2000). Typically, the high inlet pressure of a PRV is reduced through the valve, and as independent from the flow rate, this reduced pressure value can become approximately constant. In cases when the inlet pressure is lower than the outlet one, PRV behaves like a check valve, and it is completely closed. Prescott & Ulanicki (2003) modelled the dynamic behavior of PRV and proposed four different dynamic PRV schemes, i.e. (1) Full Phenomenological (2) Simplified Phenomenological (3) Behavioral, and (4) Linear Model. The first model is known to be the most realistic model. The behavioral PRV model gives similar results to the first model. Prescott & Ulanicki (2008) improved the control performance of PRV by using the behavioral model. Creaco *et al.* (2018) also used the behavioral PRV model while testing the performance of PRVs and real-time control valves during hydrant activation. Similarly, the behavioral PRV model has been adopted by Ulanicki & Beaujean (2021) by asserting a dynamic WDN model algorithm.

EPANET has been extensively used for hydraulic calculations and water quality analyses of WDNs (Rossman 2000; Rossman *et al.* 2020). Numerous studies applied PM and leakage reduction modelling with EPANET as a tool. Araujo *et al.* (2006) determined the number and position of control valves, as well as the valve settings, to minimize pressures and leakage in the network. Minimization activity is done through the genetic algorithm with the help of the EPANET hydraulic solver in this study. Marunga *et al.* (2006) applied a PM operation in the hydraulic model of Mutare City and demonstrated that when the PRV outlet pressure is reduced from 77 m to 50 m, minimum night flow (MNF) decreases about 25%. Since it is known that the MNF is an essential indicator of leakage (Thornton *et al.* 2008), the effect of PM on leakage can be recognized. Karadirek *et al.* (2012) established a hydraulic model of 18 DMAs in Antalya, Turkey, and used the hydraulic model to manage pressure and reduce leakage. Results of the study show that when the PM is appropriately applied at the field scale, the reliability and fitness of the WDN will tremendously increase due to the reduction of water losses. Parra & Krause (2017) made a PM application in Germany, and they have shown that RNM PM is more effective than Fixed Outlet PM on leakage reduction. García-Ávila *et al.* (2019) hydraulically modelled the WDN of Andean City and optimized the setting and location of PRVs in the WDN. They showed that the technical performance of the WDN is improved after optimization. Rokstad (2021) also optimized the Fixed Outlet and Flow Modulated PMs in WDNs, especially for firefighting needs in Trondheim, Norway. Rokstad's (2021) results underlined the importance of combining Fixed Outlet and Flow Modulated PMs for lower leakage compared to using only the Fixed Outlet approach.

In EPANET, pressure management can be done via the PRVs. However, the PRV definition in the original software can only produce constant outlet pressure. This constant pressure is a major concern indicating that the current EPANET hydraulic solver only uses Fixed Outlet PM. The outlet pressure graph of the PRV also displays a flat line with no fluctuations or spikes. The existence of fluctuations is a vital issue for the hydraulic model, as the pressure levels and flow rates cannot take constant values in real situations. Therefore, using a dynamic PRV scheme is essential to avoid physically inconsistent results. The current version of EPANET software does include neither dynamic PRV model nor PM type options. In the proposed study, EPANET 3's C++ code (https://github.com/OpenWaterAnalytics/epanet-dev 2016) has been modified to utilize dynamic PRV with four different PM schemes. The novelty of this study lies in the major contribution to the open-source software that can now benefit from four different pressure management plans in the hydraulic model of water distribution networks.

Note that this newly proposed version of EPANET 3 software is part of a continued work that includes the Rigid Water Column Global Gradient Algorithm (RWC-GGA) as a hydraulic solver (Koşucu 2021a). Previously, EPANET 3 had only a GGA hydraulic solver option available, unlike now. However, hydraulics of incompressible unsteady flows can be solved in the current version of EPANET (v3.1). This study focuses on adding four PM schemes to EPANET software that can solve incompressible unsteady flow hydraulics and the applicability of dynamic PRV in this software.

## HYDRAULIC SOLVER

Conventional hydraulic solver embedded in EPANET (versions of 1.0, 2.0 and 2.2), e.g. GGA, incorporates quasi-steady-state flow equations. The GGA solver can be used for extended period simulations (EPS) with temporal scales in the order of minutes (Nault 2017). However, realistic PRV simulations require unsteady flow equations due to the dynamic nature of the valves (Prescott & Ulanicki 2003; Janus & Ulanicki 2017). For this reason, we chose RWC GGA as a hydraulic solver in this study.

^{3}/s); is the length of the intermediate link (m);

*g*is the gravitational acceleration (m/s

^{2}), is the cross-sectional area of the intermediate link;

*t*is time (s). As previously stated, the term on the right-hand side of equality provides unsteadiness and is denoted as the inertial term. This term equals zero in steady flows and represents the acceleration quantity in unsteady flow conditions.

*et al.*(2012), Todini & Rossman (2013), and Nault & Karney (2016) provide additional information about the equations.

## DYNAMIC PRV MODEL

The adopted dynamic model of the PRV in the proposed study is the behavioral model of Prescott & Ulanicki (2003). As well as the phenomenological model is the most realistic PRV representation, the behavioral model gives similar results and is more applicable. The behavioral model is based on PRV's two parts: the main valve and control space. The functionality of the PRV can be defined as a hydraulic control circuit that detects the difference between the downstream pressure head (m) and the desired set point (m). When the difference value is negative, water comes out of the control space, and when it is positive, water enters here. This action happens on the occasion of the inner needle valve. In this way, PRV tries to hold the head of the downstream node constant.

^{3}/s) is flow out or into control space; (m

^{2}) is the cross-sectional area of the control space and is also a function of the valve opening; (m

^{2}/s) and (m

^{2}/s) are the needle valve response rates according to opening and closing, respectively.

*et al.*2018). It should also be noted that if the and hence the parameters take zero value, Equation (7) becomes undefined. Consequently, this condition leads to a numerical problem. To solve this numerical problem, when the becomes 0, valve status is changed to closed mode. By this means, computational robustness is preserved.

*et al.*(2018) state, , , , , , , and are not dependent to the PRV size. Whereas, magnitudes of , and get bigger, as long as the PRV upsizes.

Equations (5)–(9) are valid in all PM types except the Remote Node Modulated one. Remote Node Modulated PM has a difference only in Equation (6). and parameters in Equation (6) are identified as the outlet node pressure head of the PRV in conventional PM types. However, in RNM PM, both parameters are designated as the pressure value of the remote node, which is the critical point in the WDN. On the other hand, remains as the outlet node's pressure head in Equation (7).

## SOURCE CODE MODIFICATIONS

EPANET 3 is open-source software written by Open Source EPANET Initiative in Object-Oriented Programming based on C++ language (https://github.com/OpenWaterAnalytics/epanet-dev 2016). Hydraulic solver of the current EPANET 3 software can compute WDN hydraulics by using pressure-dependent demands (Todini 2003; Tanyimboh & Templeman 2010; Seyoum & Tanyimboh 2016), leakage flows (Cassa & Van Zyl 2014; van Zyl & Cassa 2014), and Generalized GGA (Todini 2011; Avesani *et al.* 2012; Giustolisi *et al.* 2012). Generalized GGA solves quasi-steady network hydraulics and cannot represent transients in pipelines. Thus, the current hydraulic solver of the EPANET 3 is switched to RWC GGA to simulate incompressible unsteady motions in WDNs.

To model Dynamic PRV in EPANET 3, a new function is put into the ‘project.cpp’ file, which is called from ‘epanet3.cpp’, named as ‘pressureManagement’. The information such as PM Type, reference pressure values, flow modulation curve coefficients, and remote node id are utilized in this function, and valve opening ratio is calculated through Equations (5), (6) and (9). It should be emphasized that Equation (5) is a differential equation, and as such, it is difficult to solve analytically. That is why it is discretized for numerical solution, and it becomes . After that, actual is computed by the expression . These computations are conducted in the ‘pressureManagement’ function inside the project.cpp file (Koşucu 2021b).

The flow chart of the EPANET 3 PM extension is given in Figure 1. For FO PM, fixed outlet pressure setting; for TM PM, day (07:00–24:00) and night pressure (00:00–07:00) settings; for FM PM, a, b, and c of the equation a*Q^{2} + b*Q+c = Outlet Pressure; for RNM PM, reference pressure setting and the id of the remote node are obtained from the input file. When the headlosses have been calculated in the links during hydraulic solving, headloss through the Dynamic PRV is computed in findDprvHeadLoss function with Equations (7) and (8). This new function is inside the ‘valve.cpp’ file.

Dynamic PRV definition requires a set of modifications in the EPANET 3 input file. These modifications are given in Table 1. Classic PRV in the software takes the outlet pressure as the setting. At the same time, the setting of the Dynamic PRV is the PM Type, such as FO, TM, FM, and RNM. If the PM Type is FO, the token which is following the setting is the fixed outlet pressure value. In the case of the TM setting, the required tokens are Day_Pressure and Night_Pressure, respectively. If FM is the setting, the coefficients of the flow modulation curve are needed. Lastly, in the RNM case, target pressure and the id of the remote node are necessary for the input file.

PM Type . | Token0 . | Token1 . | Token2 . | Token3 . | Token4 . | Token5 . | Token6 . | Token7 . | Token8 . |
---|---|---|---|---|---|---|---|---|---|

Classic PRV | ID | Node1 | Node2 | Diameter | Type: PRV | Setting: Outlet Pressure | MinorLoss | – | – |

DPRV-FO | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: FO | FO_Pressure | – | – |

DPRV-TM | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: TM | Day_Pressure | Night_Pressure | – |

DPRV-FM | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: FM | a_FM | b_FM | c_FM |

DPRV-RNM | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: RNM | RN_Pressure | ID of RN | – |

PM Type . | Token0 . | Token1 . | Token2 . | Token3 . | Token4 . | Token5 . | Token6 . | Token7 . | Token8 . |
---|---|---|---|---|---|---|---|---|---|

Classic PRV | ID | Node1 | Node2 | Diameter | Type: PRV | Setting: Outlet Pressure | MinorLoss | – | – |

DPRV-FO | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: FO | FO_Pressure | – | – |

DPRV-TM | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: TM | Day_Pressure | Night_Pressure | – |

DPRV-FM | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: FM | a_FM | b_FM | c_FM |

DPRV-RNM | ID | Node1 | Node2 | Diameter | Type: DPRV | Setting: RNM | RN_Pressure | ID of RN | – |

## APPLICATIONS

In this study, the Dynamic PRV model and RWC GGA have been conducted in two different WDNs. One of them belongs to Istanbul's Anatolian section (Case Study 1), and the other is extracted from Jowitt & Xu (1990) article (Case Study 2). The hydraulic and pattern time steps are adopted as 1 second and 1 minute, respectively. Both WDNs hydraulics are simulated for 24 hours period. The EPANET input files of these two WDNs, together with the source code, are publicly available (Koşucu 2021b).

### Case study 1

The WDN of the Case Study 1 is located in the Anatolian side of Istanbul city (Figure 2). The WDN has one reservoir, 275 junctions, one valve (PRV), and 334 pipes. The topography of the DMA varies mainly from west to east. While the western part of the DMA contains high-elevation nodes, the eastern part has low-elevation nodes. The leakage rate is 59.5% in the WDN, indicating that more than half of the treated water is lost. Four different PM schemes have been tested in the WDNs hydraulic model to understand PM types’ affection degree on leakage.

In the case of no PM, excessive pressures occur in the WDN. Pressure graphs of the junctions J-171, J-226, and J-655 during 24 hours are given in Figure 3. J-171 is the critical (with the highest elevation) node, J-226 is the highest pressure (with the lowest elevation) node, and J-655 is the PRV's outlet node. In no PM conditions (Figure 3), pressures at the J-226 exceed 100 m which is an unsafe value as a pressure in the WDN. Thus, PM is deemed necessary to both reduce excess pressures and leakage.

It is essential to elaborate on the parameter values determined in the implemented PM study at this stage. Parameter values of the PRV have been excerpted from Creaco *et al.* (2018), which are , , , , , , , , , and . The parameter values selected in all PM scenarios are determined so that the pressure at the critical node does not fall below the minimum allowable pressure value, i.e. 20 m. In the FO PM, PRV outlet pressure is 67 m; in the TM PM, PRV outlet pressures are 51 m during the night and 67 m during the day; in the FM PM, PRV outlet pressure is equal to a_FM*Q^{2} + b_FM*Q + c_FM, wherein a_FM is 0.001707, b_FM is 0.004721, and c_FM is 37.5177. Lastly, in the RNM PM, the remote node target pressure is 20 m, and the id of the remote node is ‘J-171’.

Since it is essential to examine the capability of the proposed EPANET code to manage pressure with the four PM methods, the methods are applied in the hydraulic model of DMA: FO PM, TM PM, FM PM, and RNM PM. In the case of FO PM (Figure 4(a)), 67 m selected outlet pressure reduces critical node's pressure to 20 m in only peak water demand hours. In other hours, the critical node's pressure is not reduced to 20 m, and excessive pressures still occur at node J-226. It is known that water demands are low and pressures are high at night hours. One of the standard PM techniques, such as time modulation, can be used to avoid excessive pressures at night hours. By this consideration, TM PM is implemented on the DMA (Figure 4(b)), and the night pressures, in this case, become 16 m lower than the corresponding FO PM pressures. Even if reducing only night pressures benefits the DMA, the highness of the day pressures still constitutes a problem. Modulating the PRV outlet pressure according to the flow is a reasonable solution to reduce pressures the whole day. In the FM PM (Figure 4(c)), PRV outlet pressure (pressure of the J-655) changes throughout the day according to the flow modulation curve. PRV outlet pressure value is directly dependent on the flow rate in this PM method. Once the flow rate is high, PRV outlet pressure also increases, and vice versa. Thus, as seen in Figure 4(c), the pressure values of the J-655 are low at night and high at the peak demand hours. Moreover, the critical node has almost 20 m pressure value during the whole day in this method.

The fourth PM method (RNM PM) aims to directly fix the remote node's pressure constant in a WDN. The remote node is usually selected as a critical node, and the opening ratio of the PRV is continuously updated to fix the pressure of this node. As seen in Figure 4(d), pressure values of the J-171 become 20 m in analogy to the FM PM.

One of the main advantages of using the Dynamic PRV is its ability to compute the valve opening ratio. In Figure 5(a)–5(d), changes in valve opening ratio (Xm) during 24 hours are given. Here, 0 means the valve is fully closed, and 1 means the valve is fully open. At first glance, it can be seen that valve opening ratios are generally low at night hours and rise during the peak demand hours in all PM types. Secondly, valve opening ratio values of the FM PM and RNM PM are smaller than FO PM and TM PM overall. As can be shown in Figures 4c and 4d, pressures in the FM PM and RNM PM are also small according to the two other PM types. Therefore, pressure graphs of the PM methods confirm the correctness of valve opening ratios.

Among four different PM types, the latter two are more advanced and more innovative than the first two since the last two PM techniques (i.e. FM and RNM) can adapt themselves to changing consumption patterns. Although these two techniques have different pressure regulation methods, they lead to similar results, i.e. Figures 4 and 5 show that the pressure graphs and valve opening ratio graphs are similar.

WDN inlet flow rate is an essential indicator of the degree of leakage. In Figure 6, the graph of the inlet flow rate related to 5 different scenarios is shown. The flow rate that enters the WDN consist of 2 components: 1. Consumer Demand Flow, 2. Leakage Flow. Leakage gets high as long as pressure increases. Thus, when the PM is applied, leakage decreases immediately. This reality can be observed in Figure 6. The highest flow rates by far belong to the NO PM scenario. Indeed, the NO PM scenario has the highest leakage among all scenarios, with a rate of 59.5%. As we mentioned before, the leakage amount is maximum at night hours. Therefore, the quality of a PM can be measured by how much it reduces leaks at night hours. FO PM and TM PM come after NO PM at night hours, as seen in Figure 6, and the leakage ratio values of the two methods are 56 and 53.9%, respectively.

It should be noted that the flow rates of FM PM and RNM PM are also similar. In other words, like pressure and valve opening ratio graphs, WDN inlet flow rates are almost identical in these two pressure management schemes. In both PM types, persistence to keep the pressure of the critical node constant at 20 m is present. Therefore, these two PM methods behave similarly and are the most effective leakage reduction strategies. The leakage rates of these two PM methods are 45.8 (FM PM) and 45.7% (RNM PM), respectively.

### Case study 2

We used an existing WDN from Jowitt & Xu (1990) to analyze the effectiveness and performance of the Dynamic PRV. The layout of this WDN is given in Figure 7, i.e. has 3 reservoirs, 22 junctions and 37 pipes. Several PRV combinations are formed in the WDN. The list of the combinations is presented in Table 2.

Scenario . | Number of Valves . | Valve Locations . | Valve Settings (m) . |
---|---|---|---|

1 | 1 | P-37 | 32 |

2 | 2 | P-37, P-01 | 32, 30 |

3 | 3 | P-37, P-40, P-41 | 33, 33, 33 |

4 | 4 | P-37, P-01, P-28, P-31 | 35, 35, 35, 35 |

Scenario . | Number of Valves . | Valve Locations . | Valve Settings (m) . |
---|---|---|---|

1 | 1 | P-37 | 32 |

2 | 2 | P-37, P-01 | 32, 30 |

3 | 3 | P-37, P-40, P-41 | 33, 33, 33 |

4 | 4 | P-37, P-01, P-28, P-31 | 35, 35, 35, 35 |

In Jowitt & Xu (1990) WDN, four different scenarios are applied depending on the number of valves. In these four scenarios, the number of valves varies between 1 and 4. FO PM is implemented in all scenarios with both Classic PRV and Dynamic PRV models. Valve outlet pressure settings are also given in Table 2. Those are changing between 32 and 35 m.

The pressure graphs of Junctions J-12 and J-22 are demonstrated in Figure 8. J-12 is the just downstream junction of pipe P-37, and J-22 is the junction on the lower right corner of the WDN. Junction J-12 is on the downstream side of pipe P-37, and adjusted pressure values belonging to the therein valve is manifested in Table 2 as 32 m, 32 m, 33 m and 35 m, respectively. In Figure 8(a), 8(c), 8(e) and 8(g), GGA simulations’ results belong to both Classic PRV (denoted as PRV in the *Figures*) and Dynamic PRV (denoted as DPRV in the *Figures*) models could be observed. As seen in the *Figures*, the pressure of the junction J-12 is constant during the simulations using the Classic PRV model. Even though this constancy provides a positive impression, it is known that when the flow rate that enters PRV devices is changed, outlet pressure is also changed rapidly. After this rapid change, the outlet pressure of PRV devices returns to its adjusted value (Prescott & Ulanicki 2003). By considering this information, it could be said that the Classic PRV model in the current EPANET versions gives improper results. However, the Dynamic PRV model constitutes factual outputs due to paying attention to this issue. For instance, pressure values drop in the Dynamic PRV model simulations when flow rates increase with rising water consumption in the morning hours (Figures 8 and 9). Following this pressure drop, the outlet pressure of the Dynamic PRV resumes converging to the Dynamic PRV's setting pressure value by rising. Substantially, simulations of the Classic PRV and the Dynamic PRV models exhibit similar results except for the expeditious flow rate alteration cases.

Besides the results of GGA as a hydraulic solver, outputs of simulations with RWC GGA solver are demonstrated in Figure 8(b), 8(d), 8(f) and 8(h). Depending on the inertial term in Equation (1) and sudden demand value changes, pressure values have a volatile behaviour throughout the whole RWC GGA simulation period. These pressure spikes (surges) are an indicator of incompressible unsteady hydraulics; however, the general trends of pressure graphs are consistent with GGA results. To exemplify, the pressure of junction J-22 decreases until 08:00 AM and increases after here in all simulations independent from the hydraulic solver type and the number of valves. A similar pattern could be observed for junction J-12.

In addition to pressure graphs of two junctions, flow graphs of three pipes (P-37, P-09, P-41) are given in Figure 9. Flow graphs are in total harmony, unlike the pressure graphs, even if the hydraulic solver is RWC GGA. Only one conspicuous issue is the difference between the Classic PRV and the Dynamic PRV simulations, especially in the 4 Valve scenario and at morning hours. Except for this slight difference, the flow rate values are in accord. The compatibility of simulation results with different hydraulic solvers and several valve configurations substantiates that the Dynamic PRV model presents coherent results in GGA and RWC GGA hydraulic solvers cases. The simulations executed with different hydraulic solvers and valve configurations are compatible with each other, showing that the analyzes made with the Dynamic PRV model are consistent.

Simulation run time is an important efficiency indicator for hydraulic models. In Table 3, simulation times with GGA and RWC GGA hydraulic solvers are present. The table shows that RWC GGA hydraulic solver increases run time between 3.8 and 11%. In 1 valve scenario increment ratio is 11%, and in 2-valve scenarios, this ratio is 3.8%. These results imply that the GGA solver is more efficient than the RWCGGA solver, and unless it is necessary, using the GGA solver is rewarding from the computational point of view.

Scenario . | Number of Valves . | GGA (sec.) . | RWCGGA (sec.) . |
---|---|---|---|

1 | 1 | 198 | 220 |

2 | 2 | 210 | 218 |

3 | 3 | 210 | 220 |

4 | 4 | 211 | 220 |

Scenario . | Number of Valves . | GGA (sec.) . | RWCGGA (sec.) . |
---|---|---|---|

1 | 1 | 198 | 220 |

2 | 2 | 210 | 218 |

3 | 3 | 210 | 220 |

4 | 4 | 211 | 220 |

## DISCUSSION

Various pressure management schemes have been tested in the EPANET literature (Vicente *et al.* 2016); however, only a fixed (not-dynamic) outlet pressure management scheme is provided with the software to the end-users. In this study, we introduced four different pressure management schemes into the source code: fixed outlet, time modulated, flow modulated, and remote node modulated pressure managements.

The time modulated scheme is appropriate for WDNs with a high difference between night and day pressures. If night pressures are not reduced, this can lead to bursts in the connections or along the pipes. The latter two schemes are appropriate if a WDN requires managing pressure according to flow or remote node characteristics. These all become available with the new code extension presented in this study.

The classic PRV definition in the current version of EPANET is not dynamic. This state of being non-dynamic is a severe deficiency in terms of not being able to reveal how valve movements change. Since the physical condition of the PRV is not determined, field studies cannot be adequately modelled. On the other hand, accurately modelling a PRV in a physically meaningful way is possible in the newly proposed EPANET PM extension. The proposed EPANET PM extension also adopts a new hydraulic solver, i.e. RWC GGA, which can model incompressible unsteady flows. These are critical contributions to the EPANET source code so that PRV dynamics can be represented and the entire WDN can be modelled accurately as a system.

It is a fact that leak losses and consumer connections are distributed along WDN pipes. Considering this fact, Giustolisi & Todini (2009) introduced a distributed demand model to GGA, and Berardi *et al.* (2010) improved this hydraulic model and named the improved model as Enhanced GGA. Afterwards, Menapace *et al.* (2018) developed the EPANET 2.0 code with the distributed demand model included. Note that RWC GGA assumes flow is the same along the pipe. The reason is that the inertial term in Equation (1) supposes a single flow value for a pipe instead of multiple flow values. Therefore, RWC GGA cannot simulate distributed demands and leaks, which reduces the algorithm's flexibility.

Even though RWC GGA can simulate gradual unsteady motions, this algorithm cannot model rapid motions in WDNs. Especially in the case of rapid demand oscillations, rigidity in water columns is abolished; therefore, only the elastic water column model becomes valid. For more robust and accurate hydraulic computations in the EPANET PM extension, the elastic water column (i.e. Water Hammer Model) algorithm must be implemented in the code. Since the elastic water column algorithm necessitates the discretization of pipes, this algorithm is more suitable than RWC GGA for modelling distributed demands and leaks.

If there are no sudden demand changes or rapid device (such as valve or pump) movements in a WDN, using GGA as a hydraulic solver is computationally more preferable than the RWC GGA solver as it is lighter in CPU time. Especially in cases where multiple simulations are required and there are no instantaneous hydraulic changes, adopting GGA as a hydraulic solver is a more appropriate algorithm choice than RWC GGA.

## CONCLUSION

In this study, new PM features have enhanced the software's source code. Since EPANET 3 is written in C++, an object-oriented programming language and convenient for modifications to add the Dynamic PRV model and four different PM schemes to the source code. We demonstrated the new features on a selected water distribution network in Istanbul, Turkey and tested its robustness in the water distribution network of Jowitt & Xu (1990), a commonly used network.

This study has shown that water losses are significantly reduced when four different PMs are applied in the hydraulic model of WDN. Also, this study has discussed the reasons for FM PM and RNM PM schemes performing better than the FO PM and TM PM schemes. One of the more significant findings to emerge from this study is that these schemes reduce the leakage rates more than the latter two methods and provide nearly constant pressure at the critical point. Although the FM PM and RNM PM schemes are highlighted here as advantageous to the other two PM methods, applying these two PM schemes in the field may not be accessible due to the high installation and operating costs. The decision-makers should consider the specific needs and conditions of WDNs when determining the most appropriate scheme that will be used in practice.

Applying different PM schemes in EPANET 3, this study is coupled with a newly introduced hydraulic solver, i.e. RWC GGA (Koşucu 2021a). RWC GGA, based upon incompressible unsteady flow hydraulics, is far suitable for designing PRVs in stable operating conditions (Janus & Ulanicki 2017). However, this hydraulic solver cannot model the distributed demands and leaks. This issue could cause inaccuracy during hydraulic simulations. Therefore, instead of using the RWC GGA hydraulic solver, adopting the elastic water column algorithm reinforced with Enhanced GGA can produce more reliable results. To simulate demands and leaks in WDNs properly, reconciling elastic water column algorithm and Enhanced GGA should be on the agenda for future works. In addition to our code enhancements, future work is necessary to determine the optimal pressure management scheme for various flow and demand patterns in WDNs.

## ACKNOWLEDGEMENTS

We acknowledge the financial support by Turkish Scientific and Technical Research Council (TÜBÍTAK) grant number 118C020 and the National Center for High-Performance Computing of Turkey (UHeM) under grant number 1007292019. The constructive review comments of Ezio Todini and two anonymous reviewers significantly improved this study. We are thankful for the contributions of Fatih Buğrahan Yorgun to the Graphical Abstract.

## COMPETING INTERESTS

The authors declare that they have no conflict of interest.

## DATA AVAILABILITY STATEMENT

All relevant data (The C++ source code of the EPANET developments and input files of the two WDNs) are publicly available from an online repository (https://zenodo.org/record/6243078#.YjF9mZahlPY).

## REFERENCES

*Pressure, Leakage and Energy Management in Water Distribution Systems*

*Ph.D. Thesis*

*Integrating Water Systems - Proceedings of the 10th International on Computing and Control for the Water Industry, CCWI 2009*

*Comprehensive Simulation of One-Dimensional Unsteady Pipe Network Hydraulics: Improved Formulations and Adaptive Hybrid Modeling*