Calibration of urban water distribution networks and investigation of different placement scenarios of pressure relief valves: A case study in Western zone of Poldokhtar-Iran

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The present research investigated hydraulic modeling, calibration, and different placement scenarios of pressure relief valves (PRV) within the Poldakhter WDN (Western zone) to solve the problems above. According to the selected objective function and the range of changes in the roughness coefficient and consumption, the optimization was conducted using the genetic algorithm (GA) inside hydraulic software. Hydraulic simulation showed that the pressure head in 18% of nodes in the network is more than 45 meters, while it is less than 15 m in 51% of the nodes. The results from the five proposed scenarios show a significant improvement regarding the WDN's performance, and pressure heads lower than 15 m can be reached in less than one percent of the network. Water distribution network Calibration Pressure measurement Genetic algorithm Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction The lack of drinking water resources, the rapid growth of demand due to population growth, and the high costs of water treatment and supply have caused many social, economical, and even political problems across numerous countries. In recent decades, one of the main concerns of water utility managers has been decreasing water loss, which often reaches 30 or even 40% of the volume of water entering the network (Krokana et al., 2016). With the development of urban areas and the expansion of WDNs, managing and operating them has become increasingly challenging. This is due to the complex nature of these networks, which consist of thousands of components, many of which are buried infrastructures in the earth. The main task of WDN is to satisfy the consumers' demand at the desired pressure and quality levels. High pressure in WDNs causes problems such as increased leakage and unwanted consumption. For this purpose, pressure management schedules are implemented using RPVs, tanks, and pumps. A practical solution for regulating pressure and water leakage is pressure relief valves (Price et al., 2022 ). Hydraulic modeling software are widely used to facilitate the design, management, and operation of WDNs. However, the model parameters, including pipe roughness coefficients and nodal demands, should be calibrated before using the hydraulic modeling software. Various research has been conducted on the subject of calibration and placement of PRVs in WDNs. Nicolini and Zovato (2009) employed the multi-objective genetic algorithm for optimizing the number, placement, and settings of PRVs in the WDN. Kang and Lancey (2011) presented a two-step sequential method for dual estimating roughness and consumption based on the weighted least squares design using field pipe flow and nodal pressure measurements. The proposed method was applied to two real WDNs. The results exhibited that the stepwise method could produce more accurate results in comparison with the simultaneous estimation method of two parameters. Zhang et al. ( 2018 ) presented an efficient numerical method for simultaneously calibrating pipe roughness and nodal consumption in water distribution networks. In this method, the least square error equation is selected as the objective function. To increase the method's efficiency, pipes and node consumption were grouped based on their physical characteristics to reduce the dimensions of the problem. The results of the proposed method in two case studies showed proper performance. Tiaji et al. (2018) presented a soft computing method based on GMDH and PSO to estimate Hazen-Williams coefficients WDNs. To this end, sufficient data on the Hazen-Williams coefficient, such as pipe diameters, pipe materials, and pipe flows, were used. The results showed that the GMDH method is more accurate than the PSO. Methei et al. (2022) investigated a new method using time-based intelligent control pressure-reducing valve simulation processes on a real WDN in South Africa. They implemented methods to analyze a two-phase comparative method for applying optimal pressure management and its efficiency indicators in measuring cost performance, leakage rate, leakage reduction, and leakage cost indicators. This research showed that pressure management is a suitable method to reduce leakage and estimate the location of bursts. Price et al. ( 2022 ) presented a novel algorithm to optimally explore the positions and deploy points of pressure-reducing valves in WDNs. The algorithm could identify pipes connected to downstream networks with pressures higher than the minimum required pressure and prioritize them as ideal locations to place PRVs. Four case studies with different ranges of complexities were selected to demonstrate the applicability of the algorithm for deriving pressure management solutions. One of the primary challenges faced by the Poldokhtar WDN, located in Lorestan Province, Iran, is insufficient water pressure, which leads to customer dissatisfaction. Consequently, in this research, calibration and different placement scenarios of PRVs along a specific area of the WDN have been investigated to solve the problems above. Materials and methods Poldokhtar is one of the cities in Lorestan Province, Iran, which is located in the southwest of this province. The population of Poldakhter and surrounding villages covered by the WDN is equal to 35000 people. The total per capita consumption in urban and rural areas was calculated as 226 and 168 liters per day, respectively. The WDN of the city includes two zones, Western and Eastern. In this research, the Western zone of the city has been investigated, indicating that the diameter of the network pipes is between 75 mm and 500 mm and the total length of the network is 34535 meters. The map of pipelines and topography was prepared by AutoCAD and this map was imported into the hydraulic analysis software. The reservoir of this zone is located at an altitude of 725 meters. The lowest point of this zone has a height of about 651 meters and the highest point of consumption node has a height of 672 meters. There are 4 pressure relief valves in this zone. The upstream pressure of these valves is between 60 and 70 meter. Upon examination of the valve pressure pattern, it was observed that the downstream pressure of the valves undergoes 10 meter from 12:00 pm to 6:00 am and 25 meter from 6:00 am to 12:00 am. Model calibration The calibration of water distribution models is a complicated task because it has many unreliable parameters, including the roughness coefficient of pipes, the water demand of nodes, and the open or closed status of pipes. In calibration with changes in the roughness coefficient, the network is divided into several groups in terms of the type of pipe. In the determined range, the model is analyzed and the most suitable roughness coefficient is selected according to the increase or decrease of pressure caused by the change of the roughness coefficient. Calibration can also be done with changes in water consumption of specified nodes. In hydraulic software, the calibration process is done using the genetic algorithm and three functions of minimizing the square of the differences, minimizing the absolute value of the differences, and minimizing the maximum of the differences (Eq. 1 to 3) are used as the objective functions of the optimization problem: $$\frac{\sum _{np=1}^{NH}{w}_{nh }{\left(\frac{{Hsim}_{nh}- {Hobs}_{nh}}{Hpnt}\right)}^{2}+ \sum _{nf=1}^{NF}{w}_{nf }{\left(\frac{{Fsim}_{nf}- {Fobs}_{nf}}{Fpnt}\right)}^{2} }{NH+NF} \left(1\right)$$ $$\frac{\sum _{np=1}^{NH}{w}_{nh }\left|\frac{{Hsim}_{nh}- {Hobs}_{nh}}{Hpnt}\right|+ \sum _{nf=1}^{NF}{w}_{nf }\left|\frac{{Fsim}_{nf}- {Fobs}_{nf}}{Fpnt}\right| }{NH+NF} \left(2\right)$$ $$\text{max}\left\{{\text{max}}_{{nh}=1}^{{NH}}{w}_{nh }\left|\frac{{Hsim}_{nh}- {Hobs}_{nh}}{Hpnt}\right| ,{\text{max}}_{{nf}=1}^{{NF}}{w}_{nf }\left|\frac{{Fsim}_{nf}- {Fobs}_{nf}}{Fpnt}\right| \right\} \left(3\right)$$ $${W}_{nh}= \frac{{Hobs}_{nh}}{\sum {Hobs}_{nh}} \left(4\right)$$ $${W}_{nf}= \frac{{Fobs}_{nf}}{\sum {Fobs}_{nf}} \left(5\right)$$ In these relationships, Hobs nh and Hsim nh are the observed and simulated hydraulic gradient at the nth node, Fobs nf and Fsim nf are the observed and calculated demand at the nth node, and Hpnt and Fpnt are the hydraulic gradient and node demand, respectively. nh is the number of hydraulic gradient observation nodes, nf is the number of flow observation nodes, and Wnh and Wnf are the normalized weight factors of the hydraulic pressure gradient and the demand of the nodes, respectively. In order to check and evaluate the results of calibrating the hydraulic analysis model in different conditions, RMSE is used in the following relationship: $$RMSE= \sqrt{\frac{\sum _{i=1}^{n}{\left(obs-sim\right)}^{2}}{2}} \left(6\right)$$ In this regard, n is the amount of data. The obs and sim values ​​are the measured and calculated values ​​of the desired parameter at point i, respectively. Discussion and results Model calibration results For model calibration, network data is needed in different design conditions as well as field measurements. First, according to prepared as built plan, 7 pressure gauges were placed in the network according to Fig. 1 . Pressure values ​​were measured 24 hours a day at the mentioned points. For calibration, the measured pressure data at 7 points was given to the model by Darwin Calibrator. The grouping of the roughness coefficient of pipes and demands of nodes were done, and the range of their changes was considered to be a maximum of 20%. According to the selected objective function and the range of changes in the roughness coefficient and demands of nodes, the optimization was done by the genetic algorithm in the software. The optimal roughness coefficient for each of the 7 selected groups was between 0.85 and 1.2. Also, the range of changes between the minimum and maximum demands of the nodes of each group was between 0.84 and 1.2. Finally, after optimizing the parameters of the model, the calibration of the hydraulic model was done, the results of which are shown in Fig. 2 . The calculated and measured pressures at 5 out of 7 points are very close to each other and have a maximum difference of 0.3 meters. The maximum difference between measured and calculated data is related to point 7 and equals 7.5 meters. The mentioned point is near the reservoir and the changes in the roughness coefficient and change in node demand did not have much effect on this point. The mean square of the errors (i.e., RSME) was equal to 2.9. The closer this index is to zero; it indicates the success of model calibration. Hydraulic simulation in existing conditions Hydraulic simulation was performed in maximum and minimum demand mode. In order to allocate demand to each of the nodes and pipes, the average consumption data of all customers with UTM coordinates in the year 1400, which was equal to 5300 customers, was used. Also, the average monthly consumption of each customer, the maximum daily coefficient, and the maximum hourly coefficient were entered into the software and as a result, the maximum hourly design flow was calculated as 122 liters per second. Considering the downstream of each pressure relief valve, there is a separate or pressure sub-zone. From the 5000 cubic meter reservoir to the upstream of these valves, there is also a sub-zone. In Fig. 3 , 5 available sub-zones are shown. The number of customers for each of the 5 sub-zones varies between 282 and 1793 customers. The input flow rate for each of these sub-areas varies between 6.5 and 39.5 liters per second under conditions of maximum consumption. The amount of flow entering these sub-areas varies between 1.3 and 7.9 liters per second in the conditions of minimum consumption (Table 1 ). Table 2 shows the downstream pressure of pressure relief valves during the day and night. Table 1 Number of subscribers, minimum and maximum consumption of each zone Row Zone Number of customers Minimum consumption Maximum consumption 1 Zone number 1 1793 7.90 39.5 2 Zone number 2 282 1.30 6.5 3 Zone number 3 1392 6.0 32.5 4 Zone number 4 1217 3.43 29.8 5 Zone number 5 617 2.80 14.2 Table 2 Downstream pressure of pressure relief valves during the day and night Row PRV No. downstream pressure from 12:00 PM to 6:00 AM (minimum consumption)- m downstream pressure from 6 am to 12 pm (maximum consumption)- m 1 1 10 25 2 2 10 25 3 3 10 25 4 4 10 25 The pressure of nodes in the maximum and minimum consumption modes are shown in Fig. 4 and Fig. 5 . In the state of maximum consumption, the maximum, average, and minimum pressure are equal to 71, 22, and 4 meters, respectively. The pressure in 18% of the network nodes is above 45 meters and in 8.8% of the points above 60 meters. These points are in places where the pressure relief valve is not considered. In a large part of the network (51% of the network nodes), due to the fact that the downstream pressure of the valves is set to two and a half bar, it is less than 15 meters. In the mode of minimum consumption, the maximum, average and minimum pressure are equal to 72, 23, and 5 meters, respectively. The value of the velocity of pipes in a state of maximum consumption is less than half a meter per second in 76% of the pipes and more than 2 meters per second in 5% of the pipes. Placement scenarios of pressure relief valves Iranian standards, with the criteria for designing urban and rural water transmission and distribution systems, state that the maximum pressure in the distribution network should not exceed 50 meters and the minimum water pressure is 14 to 24 meters of water. Therefore, the range of 14 to 50 meters of water can be the normal pressure for the water distribution network. Considering the pressure in the current conditions, it was observed that the pressure in some areas is higher or lower than the standard, and some changes can be made in them. Therefore, 5 scenarios were tested based on the two parameters of displacement of pressure relief valves and their downstream pressure. Finally, the two best scenarios were compared in terms of economic parameters. Here are two scenarios that performed better. Scenario 1 In this scenario, pressure relief valves No. 1 and No. 2 are moved from their current position to other locations, which are named pressure relief valves No. 5 and No. 6. The two marked red pipes are connected to each other. Also, the downstream pressures of pressure relief valves No. 3 and No. 6 change from 25 meter to 30 meter in the state of maximum consumption. The sub-zones of this scenario and the number of customers related to them are shown in Fig. 6 and Fig. 7 . The number of customers related to the 5 sub-zones in this scenario varies between 282 and 1934 subscribers. The input flow rate for each of these sub-areas varies between 6.5 and 42.8 liters per second under conditions of maximum consumption. The amount of input flow to these sub-areas varies between 1.3 and 8.5 liters per second under minimum consumption conditions. Table 3 shows the working pressure of the valves in scenario 1 in the hours from 12:00 pm to 6:00 am (minimum consumption) and 6:00 am to 12:00 pm (maximum consumption). Table 3 Output pressure of pressure relief valves during the day and night in scenario 1 Row PRV No. Working pressure from 12:00 PM to 6:00 AM (minimum consumption)- m Working pressure from 6 am to 12 pm (maximum consumption)- m 1 1 10 30 2 2 10 25 3 3 10 25 4 4 10 30 In the maximum consumption mode, the maximum, average, and minimum pressures are equal to 65, 1.25, and 3.6 meters, respectively. In this scenario and in the state of maximum consumption, considering that the downstream pressure of the valves is set to three times, the pressure is less than 15 meters in only 3.8% of the nodes of the network. The pressure in 9% of the network nodes is above 45 meters and in 1.4% of the points above 60 meters. In the mode of minimum consumption, the maximum, average, and minimum pressure are equal to 72, 21, and 0 meters, respectively. Scenario 2 In this scenario, pressure relief valves PRV-1 to PRV-4 are removed and a pressure relief valve called PRV-7 is added instead. A polyethylene pipeline with a diameter of 110 mm and a length of 1300 meters is directly connected to a tank of 5000 cubic meters and continues until near the pressure relief valve 4. A pressure relief valve (PRV-8) is added to this line. The two red-marked pipes are connected to each other as in the first scenario. Table 4 shows the working pressure of pressure relief valves at the time of minimum and maximum consumption. Table 4 Downstream pressure of pressure relief valves during the day and night in scenario 2 Row PRV No. Working pressure from 12:00 PM to 6:00 AM (minimum consumption)- m Working pressure from 6 am to 12 pm (maximum consumption)- m 1 7 10 25 2 8 25 40 In Fig. 8 and Fig. 9 , the position of the pressure relief valves and the sub-zones of this scenario are shown. The number of customers related to this scenario is 211 and 5086. The input flow to each of these sub-zones is 6.5 and 116 liters per second in the conditions of maximum consumption. Maximum, average and minimum pressure are equal to 54, 27, and 6 meters, respectively. The pressure in less than 1% of the nodes is above 45 meters. Also, in 1% of network nodes, the pressure is less than 15 meters. In the mode of minimum consumption, the maximum, average and minimum pressure are equal to 54, 23, and 6 meters, respectively. Top scenario: In this network, several scenarios were investigated to determine the best location of the pressure relief valve. Table 5 shows the results of the scenarios. Table 5 Proposed scenarios Scenario No. maximum consumption minimum consumption Pressure less than 14 m-% Pressure between 14-50m-% Pressure higher than 50 m-% Pressure less than 14 m-% Pressure between 14-50m-% Pressure higher than 50 m-% existing 50.3 33.7 16.0 72.6 5.0 22.4 1 3.7 90.0 6.3 41.5 45.0 13.5 2 0.7 98.5 0.7 2.5 97.0 0.5 3 54.0 45.4 0.6 75.9 23.1 1.0 4 2.5 95.7 1.8 2.5 96.8 0.7 5 5.4 89.0 5.6 12.8 75.6 11.6 By examining the pressure parameters at maximum and minimum consumption in different scenarios, scenario 1 and 2 have performed better than other scenarios. Since the economic parameter plays a very important role in infrastructure projects, the two best options were also compared from an economic point of view (Table 6 ). Table 6 Economic analysis of top scenarios ( $ ) scenario Purchase and implementation of polyethylene pipe Construction of pressure relief valve pit and installation of valves sum 1 0 2000 2000 2 8400 2000 10400 From the comparison of the best scenarios in terms of pressure and economic parameters, it can be concluded that scenario number 2 performs better in terms of pressure parameters, but scenario number one has a much lower cost in terms of economics. Conclusions In this research, a part of the water distribution network in Poldokhtar was investigated. A map of the city and all data related to the customers were obtained. Based on the available pressure relief valves, the network was divided into five pressure zones. After solving the existing problems and installing pressure gauges to check the pressure of the existing network, calibration and hydraulic modeling of the network were done. Having checked the downstream pressure pattern of each existing pressure relief valve during the day, the pressure was set at almost two and a half bars. This caused a lack of normal pressure distribution and in some areas, customers faced a lack of water pressure. Investigations and field observations showed that by changing the location of the pressure relief valves in the distribution network and adjusting their pressure based on the needs of the covered customers, the water pressure in the network can be brought to a standard state. This reduces breakage in water pipes and, on the other hand, distributes water pressure relatively equal for the customers. In conclusion, 5 proposed scenarios were examined and the best scenarios were selected from the technical and economic point of view. Declarations Author Contribution This research was a research project related to Lorestan-Iran water and sewage company, which was done with the participation of all four people.jafar mamizadeh and Seyyed Hamed Abdullahi wrote the main manuscript text , Fakhreddin Moradi Kia and Mohammad Mehdi Riyahihelped for the field measurement and english editing. References Covelli C, Cozzolino L, Cimorelli L, Della Morte R, Pianese D (2016) Optimal Location and Setting of PRVs in WDS for Leakage Minimization. Water Resources Management 30(5):1803-1817 De Paola F, Galdiero E, Giugni M (2017) Location and Setting of Valves in Water Distribution Networks Using a Harmony Search Approach. Journal of Water Resources Planning and Management 143: 6 El-Zahab S, Zayed T (2019) Leak detection in water distribution networks: an introductory overview. Smart Water 4 (5): 1-23 Kang D, Lansey K (2011) Demand and roughness estimation in water distribution systems. Journal of Water Resources Planning and Management 137(1):20-30 Korkana P, Kanakoudis V, Patelis M, Gonelas K (2016) Forming district metered areas in a water distribution network using genetic algorithms. Procedia Engineering 162: 511 – 520 Mathye R.P, Scholz M, Nyende-Byakika S (2022) Optimal Pressure Management in Water Distribution Systems: Efficiency Indexes for Volumetric Cost Performance, Consumption and Linear Leakage Measurements. Water 14(5): 805 Nicolini M, Zovatto L (2009) Optimal location and control of pressure reducing valves in water networks. Journal of Water Resources Planning and Management, ASCE 135(3):178-187 Price E, Abhijith R.G, Ostfeld A (2022) Pressure management in water distribution systems through PRVs optimal placement and settings. Water Research 226: 119236 Tyagi D. K, Majumder M, Kant C, Singh A. P (2018) Estimation of Hazen Williams’s constant for a residential water distribution network; GMDH and PSO approach. International Journal of Engineering and Technology 7: 92-99 Zhang Q, Zheng F, Duan H. F, Jia Y, Zhang T, Guo X (2018) Efficient numerical approach for simultaneous calibration of pipe roughness coefficients and nodal demands for water distribution systems. Journal of Water Resources Planning and Management 144(10) Bhave P.R (2003) Optimal Design of Water Distribution Networks. 1st Ed., Alpha 4 Motley Bentley Systems Incorporated (2022) WaterGEMS users guide. Water distribution design and modeling, fundamentals.Bentley Institute Course Guide, USA Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3716214","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":257821026,"identity":"54c7884f-df2e-4167-b7b3-76e918ed0c5c","order_by":0,"name":"Jafar Mamizadeh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYBACxgYQaQDEB3gYHyQUQIUTiNTCbJBgQIQWBDjAwybBYEBYHQNzA3fipxsFdfJ8x3uPVTwwsItmYD/8gOHhHnwO490snWPAZjjzzLm0GwkGybkNPGkGDAnP8GrZANTCw7jhRo4ZUAtzbgNDDtAvB/Db8jvHQMJ+w/03ZgUJBvW5DfxvCGrZBrTFIHHDDR4zhgSDw7kNEoRsaebdZp1jkJA880yOsUSCwfHcNolnBgfwaTFs7918O+dPnW3f8TOGH39UVOf28yc/fPgDn5ZmdBE2IMajgYFBHp/kKBgFo2AUjAIwAADiHlGyQ/ilKgAAAABJRU5ErkJggg==","orcid":"","institution":"Ilam University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jafar","middleName":"","lastName":"Mamizadeh","suffix":""},{"id":257821029,"identity":"9eeee28c-10db-45c9-bce7-69798cea39e8","order_by":1,"name":"Seyyed Hamed Abdullahi","email":"","orcid":"","institution":"Ilam University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Seyyed","middleName":"Hamed","lastName":"Abdullahi","suffix":""},{"id":257821033,"identity":"cacd6f8b-d8d0-4fad-84dc-dd790e961ec3","order_by":2,"name":"Fakhreddin Moradi Kia","email":"","orcid":"","institution":"Shahid Chamran University of Ahvaz","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Fakhreddin","middleName":"Moradi","lastName":"Kia","suffix":""},{"id":257821035,"identity":"1e527cf7-5a81-4043-9119-0f3a71275f54","order_by":3,"name":"Mohammad Mehdi Riyahi","email":"","orcid":"","institution":"Shahid Chamran University of Ahvaz","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"Mehdi","lastName":"Riyahi","suffix":""}],"badges":[],"createdAt":"2023-12-06 17:14:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3716214/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3716214/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":47995676,"identity":"71100c19-161e-485e-bd23-63d95fdd4e90","added_by":"auto","created_at":"2023-12-11 15:21:30","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":92181,"visible":true,"origin":"","legend":"\u003cp\u003eThe position of pressure measurement stations in the network\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/f615ad7036671584b225a49f.png"},{"id":47990439,"identity":"1e88604b-2f92-401f-9487-ba041f43e539","added_by":"auto","created_at":"2023-12-11 15:13:30","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":45050,"visible":true,"origin":"","legend":"\u003cp\u003eMeasured, simulated and optimized pressure results\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/ba3b9c108516bf5a86870de6.png"},{"id":47995680,"identity":"33a34d13-07c5-45ec-bea7-30d8faf5b523","added_by":"auto","created_at":"2023-12-11 15:21:30","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":33667,"visible":true,"origin":"","legend":"\u003cp\u003eNetwork zoning map in the existing conditions\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/7d7ba3fda0796770fdb59e60.png"},{"id":47997546,"identity":"1623759b-4724-4862-9dc6-5aa8c010f93e","added_by":"auto","created_at":"2023-12-11 15:29:30","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":48547,"visible":true,"origin":"","legend":"\u003cp\u003eThe pressure of nodes in the existing conditions - maximum consumption\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/025b59b63e7161a68228a2e5.png"},{"id":47990441,"identity":"6b121de4-db86-43c5-b70a-7927dbac91d1","added_by":"auto","created_at":"2023-12-11 15:13:30","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":50443,"visible":true,"origin":"","legend":"\u003cp\u003eThe pressure of nodes in the existing conditions - minimum consumption\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/0f2d5d785b22f9e1c7139dcb.png"},{"id":47997547,"identity":"217ce3e3-4b4c-4f35-8633-41d2e7bc60fc","added_by":"auto","created_at":"2023-12-11 15:29:30","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":68212,"visible":true,"origin":"","legend":"\u003cp\u003ePosition of pressure relief valves and change of pipe connection in scenario 1\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/bebc4b6fa5e220b6fd929e12.png"},{"id":47990433,"identity":"1704c748-ba55-475f-a2b6-4e90f1af3a7f","added_by":"auto","created_at":"2023-12-11 15:13:30","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":20690,"visible":true,"origin":"","legend":"\u003cp\u003eZoning map in scenario 1\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/199f1da9c00c778f15827a9a.png"},{"id":47990436,"identity":"fd9dbc19-567a-4422-923e-67dfb6fbfb6a","added_by":"auto","created_at":"2023-12-11 15:13:30","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":99166,"visible":true,"origin":"","legend":"\u003cp\u003eThe position of pressure relief valves in scenario 2.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/37478b57b090c7e352c39ead.png"},{"id":47995678,"identity":"38890b8a-e0a4-4460-bb6d-72882446085b","added_by":"auto","created_at":"2023-12-11 15:21:30","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":30562,"visible":true,"origin":"","legend":"\u003cp\u003eZoning map in scenario 2\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/d9bb1ef424917db0d7221ce8.png"},{"id":47998261,"identity":"688d9a35-96ca-4371-bc15-2482f7f7b244","added_by":"auto","created_at":"2023-12-11 15:37:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":846467,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3716214/v1/a60f6b03-ee07-4c1a-a370-b29390c33d05.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Calibration of urban water distribution networks and investigation of different placement scenarios of pressure relief valves: A case study in Western zone of Poldokhtar-Iran","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe lack of drinking water resources, the rapid growth of demand due to population growth, and the high costs of water treatment and supply have caused many social, economical, and even political problems across numerous countries. In recent decades, one of the main concerns of water utility managers has been decreasing water loss, which often reaches 30 or even 40% of the volume of water entering the network (Krokana et al., 2016). With the development of urban areas and the expansion of WDNs, managing and operating them has become increasingly challenging. This is due to the complex nature of these networks, which consist of thousands of components, many of which are buried infrastructures in the earth. The main task of WDN is to satisfy the consumers' demand at the desired pressure and quality levels. High pressure in WDNs causes problems such as increased leakage and unwanted consumption. For this purpose, pressure management schedules are implemented using RPVs, tanks, and pumps. A practical solution for regulating pressure and water leakage is pressure relief valves (Price et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Hydraulic modeling software are widely used to facilitate the design, management, and operation of WDNs. However, the model parameters, including pipe roughness coefficients and nodal demands, should be calibrated before using the hydraulic modeling software.\u003c/p\u003e \u003cp\u003eVarious research has been conducted on the subject of calibration and placement of PRVs in WDNs. Nicolini and Zovato (2009) employed the multi-objective genetic algorithm for optimizing the number, placement, and settings of PRVs in the WDN. Kang and Lancey (2011) presented a two-step sequential method for dual estimating roughness and consumption based on the weighted least squares design using field pipe flow and nodal pressure measurements. The proposed method was applied to two real WDNs. The results exhibited that the stepwise method could produce more accurate results in comparison with the simultaneous estimation method of two parameters. Zhang et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) presented an efficient numerical method for simultaneously calibrating pipe roughness and nodal consumption in water distribution networks. In this method, the least square error equation is selected as the objective function. To increase the method's efficiency, pipes and node consumption were grouped based on their physical characteristics to reduce the dimensions of the problem. The results of the proposed method in two case studies showed proper performance. Tiaji et al. (2018) presented a soft computing method based on GMDH and PSO to estimate Hazen-Williams coefficients WDNs. To this end, sufficient data on the Hazen-Williams coefficient, such as pipe diameters, pipe materials, and pipe flows, were used. The results showed that the GMDH method is more accurate than the PSO. Methei et al. (2022) investigated a new method using time-based intelligent control pressure-reducing valve simulation processes on a real WDN in South Africa. They implemented methods to analyze a two-phase comparative method for applying optimal pressure management and its efficiency indicators in measuring cost performance, leakage rate, leakage reduction, and leakage cost indicators. This research showed that pressure management is a suitable method to reduce leakage and estimate the location of bursts. Price et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) presented a novel algorithm to optimally explore the positions and deploy points of pressure-reducing valves in WDNs. The algorithm could identify pipes connected to downstream networks with pressures higher than the minimum required pressure and prioritize them as ideal locations to place PRVs. Four case studies with different ranges of complexities were selected to demonstrate the applicability of the algorithm for deriving pressure management solutions.\u003c/p\u003e \u003cp\u003eOne of the primary challenges faced by the Poldokhtar WDN, located in Lorestan Province, Iran, is insufficient water pressure, which leads to customer dissatisfaction. Consequently, in this research, calibration and different placement scenarios of PRVs along a specific area of the WDN have been investigated to solve the problems above.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cp\u003ePoldokhtar is one of the cities in Lorestan Province, Iran, which is located in the southwest of this province. The population of Poldakhter and surrounding villages covered by the WDN is equal to 35000 people. The total per capita consumption in urban and rural areas was calculated as 226 and 168 liters per day, respectively. The WDN of the city includes two zones, Western and Eastern. In this research, the Western zone of the city has been investigated, indicating that the diameter of the network pipes is between 75 mm and 500 mm and the total length of the network is 34535 meters. The map of pipelines and topography was prepared by AutoCAD and this map was imported into the hydraulic analysis software. The reservoir of this zone is located at an altitude of 725 meters. The lowest point of this zone has a height of about 651 meters and the highest point of consumption node has a height of 672 meters. There are 4 pressure relief valves in this zone. The upstream pressure of these valves is between 60 and 70 meter. Upon examination of the valve pressure pattern, it was observed that the downstream pressure of the valves undergoes 10 meter from 12:00 pm to 6:00 am and 25 meter from 6:00 am to 12:00 am.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eModel calibration\u003c/h2\u003e \u003cp\u003eThe calibration of water distribution models is a complicated task because it has many unreliable parameters, including the roughness coefficient of pipes, the water demand of nodes, and the open or closed status of pipes. In calibration with changes in the roughness coefficient, the network is divided into several groups in terms of the type of pipe. In the determined range, the model is analyzed and the most suitable roughness coefficient is selected according to the increase or decrease of pressure caused by the change of the roughness coefficient. Calibration can also be done with changes in water consumption of specified nodes. In hydraulic software, the calibration process is done using the genetic algorithm and three functions of minimizing the square of the differences, minimizing the absolute value of the differences, and minimizing the maximum of the differences (Eq.\u0026nbsp;1 to 3) are used as the objective functions of the optimization problem:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\frac{\\sum _{np=1}^{NH}{w}_{nh }{\\left(\\frac{{Hsim}_{nh}- {Hobs}_{nh}}{Hpnt}\\right)}^{2}+ \\sum _{nf=1}^{NF}{w}_{nf }{\\left(\\frac{{Fsim}_{nf}- {Fobs}_{nf}}{Fpnt}\\right)}^{2} }{NH+NF} \\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\frac{\\sum _{np=1}^{NH}{w}_{nh }\\left|\\frac{{Hsim}_{nh}- {Hobs}_{nh}}{Hpnt}\\right|+ \\sum _{nf=1}^{NF}{w}_{nf }\\left|\\frac{{Fsim}_{nf}- {Fobs}_{nf}}{Fpnt}\\right| }{NH+NF} \\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\text{max}\\left\\{{\\text{max}}_{{nh}=1}^{{NH}}{w}_{nh }\\left|\\frac{{Hsim}_{nh}- {Hobs}_{nh}}{Hpnt}\\right| ,{\\text{max}}_{{nf}=1}^{{NF}}{w}_{nf }\\left|\\frac{{Fsim}_{nf}- {Fobs}_{nf}}{Fpnt}\\right| \\right\\} \\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${W}_{nh}= \\frac{{Hobs}_{nh}}{\\sum {Hobs}_{nh}} \\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$${W}_{nf}= \\frac{{Fobs}_{nf}}{\\sum {Fobs}_{nf}} \\left(5\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn these relationships, Hobs\u003csub\u003enh\u003c/sub\u003e and Hsim\u003csub\u003enh\u003c/sub\u003e are the observed and simulated hydraulic gradient at the nth node, Fobs\u003csub\u003enf\u003c/sub\u003e and Fsim\u003csub\u003enf\u003c/sub\u003e are the observed and calculated demand at the nth node, and Hpnt and Fpnt are the hydraulic gradient and node demand, respectively. nh is the number of hydraulic gradient observation nodes, nf is the number of flow observation nodes, and Wnh and Wnf are the normalized weight factors of the hydraulic pressure gradient and the demand of the nodes, respectively. In order to check and evaluate the results of calibrating the hydraulic analysis model in different conditions, RMSE is used in the following relationship:\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$RMSE= \\sqrt{\\frac{\\sum _{i=1}^{n}{\\left(obs-sim\\right)}^{2}}{2}} \\left(6\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this regard, n is the amount of data. The obs and sim values ​​are the measured and calculated values ​​of the desired parameter at point i, respectively.\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion and results","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eModel calibration results\u003c/h2\u003e \u003cp\u003eFor model calibration, network data is needed in different design conditions as well as field measurements. First, according to prepared as built plan, 7 pressure gauges were placed in the network according to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePressure values ​​were measured 24 hours a day at the mentioned points. For calibration, the measured pressure data at 7 points was given to the model by Darwin Calibrator. The grouping of the roughness coefficient of pipes and demands of nodes were done, and the range of their changes was considered to be a maximum of 20%. According to the selected objective function and the range of changes in the roughness coefficient and demands of nodes, the optimization was done by the genetic algorithm in the software. The optimal roughness coefficient for each of the 7 selected groups was between 0.85 and 1.2. Also, the range of changes between the minimum and maximum demands of the nodes of each group was between 0.84 and 1.2. Finally, after optimizing the parameters of the model, the calibration of the hydraulic model was done, the results of which are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The calculated and measured pressures at 5 out of 7 points are very close to each other and have a maximum difference of 0.3 meters. The maximum difference between measured and calculated data is related to point 7 and equals 7.5 meters. The mentioned point is near the reservoir and the changes in the roughness coefficient and change in node demand did not have much effect on this point. The mean square of the errors (i.e., RSME) was equal to 2.9. The closer this index is to zero; it indicates the success of model calibration.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eHydraulic simulation in existing conditions\u003c/h2\u003e \u003cp\u003eHydraulic simulation was performed in maximum and minimum demand mode. In order to allocate demand to each of the nodes and pipes, the average consumption data of all customers with UTM coordinates in the year 1400, which was equal to 5300 customers, was used. Also, the average monthly consumption of each customer, the maximum daily coefficient, and the maximum hourly coefficient were entered into the software and as a result, the maximum hourly design flow was calculated as 122 liters per second. Considering the downstream of each pressure relief valve, there is a separate or pressure sub-zone. From the 5000 cubic meter reservoir to the upstream of these valves, there is also a sub-zone. In Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e available sub-zones are shown.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe number of customers for each of the 5 sub-zones varies between 282 and 1793 customers. The input flow rate for each of these sub-areas varies between 6.5 and 39.5 liters per second under conditions of maximum consumption. The amount of flow entering these sub-areas varies between 1.3 and 7.9 liters per second in the conditions of minimum consumption (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the downstream pressure of pressure relief valves during the day and night.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNumber of subscribers, minimum and maximum consumption of each zone\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of customers\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMinimum consumption\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMaximum consumption\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone number 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1793\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e39.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone number 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone number 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1392\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e32.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone number 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1217\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e29.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone number 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e617\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDownstream pressure of pressure relief valves during the day and night\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePRV No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003edownstream pressure from 12:00 PM to 6:00 AM (minimum consumption)- m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003edownstream pressure from 6 am to 12 pm (maximum consumption)- m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe pressure of nodes in the maximum and minimum consumption modes are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. In the state of maximum consumption, the maximum, average, and minimum pressure are equal to 71, 22, and 4 meters, respectively. The pressure in 18% of the network nodes is above 45 meters and in 8.8% of the points above 60 meters. These points are in places where the pressure relief valve is not considered. In a large part of the network (51% of the network nodes), due to the fact that the downstream pressure of the valves is set to two and a half bar, it is less than 15 meters. In the mode of minimum consumption, the maximum, average and minimum pressure are equal to 72, 23, and 5 meters, respectively. The value of the velocity of pipes in a state of maximum consumption is less than half a meter per second in 76% of the pipes and more than 2 meters per second in 5% of the pipes.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003ePlacement scenarios of pressure relief valves\u003c/h2\u003e \u003cp\u003eIranian standards, with the criteria for designing urban and rural water transmission and distribution systems, state that the maximum pressure in the distribution network should not exceed 50 meters and the minimum water pressure is 14 to 24 meters of water. Therefore, the range of 14 to 50 meters of water can be the normal pressure for the water distribution network. Considering the pressure in the current conditions, it was observed that the pressure in some areas is higher or lower than the standard, and some changes can be made in them. Therefore, 5 scenarios were tested based on the two parameters of displacement of pressure relief valves and their downstream pressure. Finally, the two best scenarios were compared in terms of economic parameters. Here are two scenarios that performed better.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eScenario 1\u003c/h2\u003e \u003cp\u003eIn this scenario, pressure relief valves No. 1 and No. 2 are moved from their current position to other locations, which are named pressure relief valves No. 5 and No. 6. The two marked red pipes are connected to each other. Also, the downstream pressures of pressure relief valves No. 3 and No. 6 change from 25 meter to 30 meter in the state of maximum consumption. The sub-zones of this scenario and the number of customers related to them are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe number of customers related to the 5 sub-zones in this scenario varies between 282 and 1934 subscribers. The input flow rate for each of these sub-areas varies between 6.5 and 42.8 liters per second under conditions of maximum consumption. The amount of input flow to these sub-areas varies between 1.3 and 8.5 liters per second under minimum consumption conditions. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the working pressure of the valves in scenario 1 in the hours from 12:00 pm to 6:00 am (minimum consumption) and 6:00 am to 12:00 pm (maximum consumption).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOutput pressure of pressure relief valves during the day and night in scenario 1\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePRV No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWorking pressure from 12:00 PM to 6:00 AM (minimum consumption)- m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWorking pressure from 6 am to 12 pm (maximum consumption)- m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn the maximum consumption mode, the maximum, average, and minimum pressures are equal to 65, 1.25, and 3.6 meters, respectively. In this scenario and in the state of maximum consumption, considering that the downstream pressure of the valves is set to three times, the pressure is less than 15 meters in only 3.8% of the nodes of the network. The pressure in 9% of the network nodes is above 45 meters and in 1.4% of the points above 60 meters. In the mode of minimum consumption, the maximum, average, and minimum pressure are equal to 72, 21, and 0 meters, respectively.\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003eScenario 2\u003c/h2\u003e \u003cp\u003eIn this scenario, pressure relief valves PRV-1 to PRV-4 are removed and a pressure relief valve called PRV-7 is added instead. A polyethylene pipeline with a diameter of 110 mm and a length of 1300 meters is directly connected to a tank of 5000 cubic meters and continues until near the pressure relief valve 4. A pressure relief valve (PRV-8) is added to this line. The two red-marked pipes are connected to each other as in the first scenario. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the working pressure of pressure relief valves at the time of minimum and maximum consumption.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDownstream pressure of pressure relief valves during the day and night in scenario 2\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePRV No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWorking pressure from 12:00 PM to 6:00 AM (minimum consumption)- m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWorking pressure from 6 am to 12 pm (maximum consumption)- m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the position of the pressure relief valves and the sub-zones of this scenario are shown.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe number of customers related to this scenario is 211 and 5086. The input flow to each of these sub-zones is 6.5 and 116 liters per second in the conditions of maximum consumption. Maximum, average and minimum pressure are equal to 54, 27, and 6 meters, respectively. The pressure in less than 1% of the nodes is above 45 meters. Also, in 1% of network nodes, the pressure is less than 15 meters. In the mode of minimum consumption, the maximum, average and minimum pressure are equal to 54, 23, and 6 meters, respectively.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003eTop scenario:\u003c/h2\u003e \u003cp\u003eIn this network, several scenarios were investigated to determine the best location of the pressure relief valve. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the results of the scenarios.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eProposed scenarios\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eScenario No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003emaximum consumption\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eminimum consumption\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePressure less than 14 m-%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePressure between 14-50m-%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePressure higher than 50 m-%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePressure less than 14 m-%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePressure between 14-50m-%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePressure higher than 50 m-%\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eexisting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e50.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e33.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e72.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e22.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e90.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e41.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e13.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e98.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e97.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e54.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e75.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e23.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e95.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e96.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e89.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e75.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e11.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBy examining the pressure parameters at maximum and minimum consumption in different scenarios, scenario 1 and 2 have performed better than other scenarios. Since the economic parameter plays a very important role in infrastructure projects, the two best options were also compared from an economic point of view (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEconomic analysis of top scenarios (\u003cspan\u003e$\u003c/span\u003e)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003escenario\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePurchase and implementation of polyethylene pipe\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eConstruction of pressure relief valve pit and installation of valves\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003esum\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10400\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFrom the comparison of the best scenarios in terms of pressure and economic parameters, it can be concluded that scenario number 2 performs better in terms of pressure parameters, but scenario number one has a much lower cost in terms of economics.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn this research, a part of the water distribution network in Poldokhtar was investigated. A map of the city and all data related to the customers were obtained. Based on the available pressure relief valves, the network was divided into five pressure zones. After solving the existing problems and installing pressure gauges to check the pressure of the existing network, calibration and hydraulic modeling of the network were done. Having checked the downstream pressure pattern of each existing pressure relief valve during the day, the pressure was set at almost two and a half bars. This caused a lack of normal pressure distribution and in some areas, customers faced a lack of water pressure. Investigations and field observations showed that by changing the location of the pressure relief valves in the distribution network and adjusting their pressure based on the needs of the covered customers, the water pressure in the network can be brought to a standard state. This reduces breakage in water pipes and, on the other hand, distributes water pressure relatively equal for the customers. In conclusion, 5 proposed scenarios were examined and the best scenarios were selected from the technical and economic point of view.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eThis research was a research project related to Lorestan-Iran water and sewage company, which was done with the participation of all four people.jafar mamizadeh and Seyyed Hamed Abdullahi wrote the main manuscript text , Fakhreddin Moradi Kia and Mohammad Mehdi Riyahihelped for the field measurement and english editing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eCovelli C, Cozzolino L, Cimorelli L, Della Morte R, Pianese D (2016) Optimal Location and Setting of PRVs in WDS for Leakage Minimization. Water Resources Management 30(5):1803-1817\u003c/li\u003e\n \u003cli\u003eDe Paola F,\u0026nbsp;Galdiero E, Giugni M (2017) Location and Setting of Valves in Water Distribution Networks Using a Harmony Search Approach.\u0026nbsp;Journal of Water Resources Planning and Management 143: 6\u003c/li\u003e\n \u003cli\u003eEl-Zahab S, Zayed T (2019) Leak detection in water distribution networks: an introductory overview. Smart Water\u0026nbsp;\u0026nbsp;4 (5): 1-23\u003c/li\u003e\n \u003cli\u003eKang D, Lansey K (2011) Demand and roughness estimation in water distribution systems. Journal of Water Resources Planning and Management 137(1):20-30\u003c/li\u003e\n \u003cli\u003eKorkana P, Kanakoudis V, Patelis M, Gonelas K (2016) Forming district metered areas in a water distribution network using genetic algorithms. Procedia Engineering 162: 511 \u0026ndash; 520\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eMathye R.P, Scholz \u0026nbsp;M, Nyende-Byakika S\u0026nbsp;(2022) Optimal Pressure Management in Water Distribution Systems: Efficiency Indexes for Volumetric Cost Performance, Consumption and Linear Leakage Measurements. Water 14(5): 805\u003c/li\u003e\n \u003cli\u003eNicolini M, Zovatto L (2009) Optimal location and control of pressure reducing valves in water networks. Journal of Water Resources Planning and Management, ASCE 135(3):178-187\u003c/li\u003e\n \u003cli\u003ePrice E, Abhijith R.G, Ostfeld A (2022) Pressure management in water distribution systems through PRVs optimal placement and settings. Water Research 226: 119236\u003c/li\u003e\n \u003cli\u003eTyagi D. K, Majumder M, Kant C, Singh A. P (2018) Estimation of Hazen Williams\u0026rsquo;s constant for a residential water distribution network; GMDH and PSO approach. International Journal of Engineering and Technology 7: 92-99\u003c/li\u003e\n \u003cli\u003eZhang Q, Zheng F, Duan H. F, Jia Y, Zhang T, Guo X (2018) Efficient numerical approach for simultaneous calibration of pipe roughness coefficients and nodal demands for water distribution systems. Journal of Water Resources Planning and Management 144(10)\u003c/li\u003e\n \u003cli\u003eBhave P.R (2003) Optimal Design of Water Distribution Networks. 1st Ed., Alpha 4 Motley\u003c/li\u003e\n \u003cli\u003eBentley Systems Incorporated (2022) WaterGEMS users guide. Water distribution design and modeling, fundamentals.Bentley Institute Course Guide, USA\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Water distribution network, Calibration, Pressure measurement, Genetic algorithm","lastPublishedDoi":"10.21203/rs.3.rs-3716214/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3716214/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOne of the most critical problems of water distribution networks (WDNs) in Iran is the lack of water pressure in the network and the lack of satisfaction from the customers. The present research investigated hydraulic modeling, calibration, and different placement scenarios of pressure relief valves (PRV) within the Poldakhter WDN (Western zone) to solve the problems above. According to the selected objective function and the range of changes in the roughness coefficient and consumption, the optimization was conducted using the genetic algorithm (GA) inside hydraulic software. Hydraulic simulation showed that the pressure head in 18% of nodes in the network is more than 45 meters, while it is less than 15 m in 51% of the nodes. The results from the five proposed scenarios show a significant improvement regarding the WDN's performance, and pressure heads lower than 15 m can be reached in less than one percent of the network.\u003c/p\u003e","manuscriptTitle":"Calibration of urban water distribution networks and investigation of different placement scenarios of pressure relief valves: A case study in Western zone of Poldokhtar-Iran","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-12-11 15:13:23","doi":"10.21203/rs.3.rs-3716214/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5c334db5-8e3e-4979-8def-e740d0c6a0eb","owner":[],"postedDate":"December 11th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-12-11T15:13:25+00:00","versionOfRecord":[],"versionCreatedAt":"2023-12-11 15:13:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3716214","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3716214","identity":"rs-3716214","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}