Numerical modeling and rational methods of water supply network operations in environmental engineering systems

This research paper uses a numerical modeling process to recreate the actual operating conditions of the water distribution system in the town of Kleosin, located on the border with Bialystok. The performed calculations allowed for the creation of a model for the functioning of the water supply network and for taking rational and optimal decisions affecting the effective operation of the entire system. The numerical modeling process is presented as a common tool to rationally and optimally manage the water distribution system. At the same time, numerous possibilities of computationally modeling and processing accurate real data were presented. The scope of the study included the network model analyzed in terms of the basic quality parameters that the network should meet, such as flow velocity, pressure, unit losses, water age, and operating conditions during simulated events, such as expansion or system failure, broken down into assumed time variants. As part of the paper, a situational variant was presented, which concerned the planned modernization in order to improve the functioning of the system by extending water distribution with new sections. The Epanet computer program distributed by US EPA was used in the research.


Introduction
Advances in science and technology as well as environmental issues mean that the emphasis on the development of water supply systems is becoming more and more popular and results in the implementation of tools supporting the modeling and monitoring of water supply networks in the form of specialized engineering programs. Modeling, according to Habib (Habib et al. 2013), deals with the construction and study of models (i.e., systems, processes, phenomena) reflecting reality or its fragment. In operation, modeling is the basic and general procedure that is used for research to determine the behavior of operational reality under given conditions. In water supply systems, appropriately created software is used to create a simple network model (Kowalska and Kowalski et al. 2017). The development of numerical modeling of water supply systems is the subject of study in numerous research centers and universities around the world, and such research is also being conducted in Poland. Epanet, WaterGEMS, and MikeNet models are well known and widely used in numerical simulations (Hołota and Kowalska et al. 2018). Such a model maps the actual water supply network on the basis of which a given water supply system can be monitored, modeled and simulated (Boulos and Ormsbee 2009). The use of a computer model of the water distribution system is as allows: • Hydraulic analysis and assessment of the current technical condition of the system, (Zimoch and Łobos 2010) • Rationalization of system functioning parameters, (Alegre et al. 2012). • Developing a forward-looking development strategy and assessing the effects of design and operational decisions taken before implementation, • Observing the work of objects, devices, and installations as well as hydraulic parameters of the network such as water pressure, speed, flow rate, and direction. (Alperovits andShamir 1977, Kowalska et al. 2018), • Modeling changes in water quality in the network, which is currently a very important issue from the point of view 1 3 18 Page 2 of 10 of the use of calibrated models. (Zimoch andBartkiewicz 2018a, 2019).
These tasks are the key to the proper functioning and the proper performance of these services involves the proper operation of the water supply system.
The main objective of the research was to prepare new, more rational ways of operating the system, including reducing the pressure value, as well as selecting and carrying out on the basis of assumed variants the most favorable conditions for the modernization or expansion of the water supply network. The designated tasks were performed with particular attention as to the accuracy of the system analysis, by distinguishing the most dangerous places in the network.

Emergency events and their influence on network functioning
On occasions, various emergency situations occur during the operation of the water supply network. They have a negative impact on the operation of the entire system and its ability to fulfill the basic functions of the water supply network. The most common damages are: • Longitudinal and transverse cracks, • Pushing out the seal, • Corrosion pits, • Destruction of welds, • Loosening the stuffing box seal behind the valves, • Closed valves in hydrants.
Many factors affect the risks to the water supply network. The first is due to errors made at the design stage, such as: • Incorrect location of network sections (incorrect recognition of ground conditions, incorrect selection of the water supply route), • Improper standard of design solutions (wrong choice of fittings, automation, corrosion protection, errors in hydraulic solutions; lack or incomplete as-built documentation).
Some of these problems are attempting to be solved by using optimizations, simulations, and algorithms. (Walski et al. 2011, Studziński 2014. Errors made during the operation of the water supply are an additional threat to waterworks. The most important irregularities include incorrect procedures, no monitoring of network operation, no response to small water leaks, or no emergency water supply. (Todini 2000;Ramos et al. 2020).
Actions aimed at reducing negative effects require impact assessment and knowledge of the layout of the water supply network, which significantly facilitates operation of the network. These activities include, among others, increasing the efficiency of other intakes or making appropriate switches on the network. (Romano et al. 2014).
Basic actions to reduce negative effects require assessment and knowledge of the water supply system, which significantly facilitate any beneficial changes made to the network. In such situations, numerical modeling and the use of computer analytical tools become necessary. Examples include determining zones exposed to increased concentrations of nitrates in water (Zimoch and Paciej 2018), the use of regression models in the analysis of a crisis situation related to the lack of consumer water supply (Pietrucha-Urbanik 2014) or the use of threat prediction based on Markov latent effect modeling (MLE) (Vincent Tidwell et al. 2005) that support making the most accurate operational decisions. At the same time, they emphasize the importance of simulation packages of hydraulic models used in the decision-making process. At the same time, this is an argument for the need to build simulation hydraulic models. (Zimoch 2008).

Description of the research subject
Kleosin is a village in the Podlaskie Province, located at the border with Bialystok. The neighborhood is a flat landscape, varied with loosely scattered hills and partly forested. Kleosin, which is inhabited by approximately 5,700 people, had its water distribution system tested. The water supply network is supplied from one intake, and the average daily water consumption is 821.11 m 3 /d, a characteristic feature is the constant increase in the amount of water supplied, observed over the years 2016-2019. The water supply network is completed from PVC pipes.
The system supplies 98.2% of the water to the village of Kleosin. The length of the active distribution network is 10.8 km. A characteristic feature of this water supply network is the water consumption that has been increasing in recent years. The intake from the intake in 2018 amounted to 234,982 m 3 , and a year later the value of water intake increased by about 13% and amounted to 266,472 m 3 (Fig.  1).
Water to the network is supplied from one (built in 2017) SW-3 deep well with an operational capacity of 100 m 3 /h. The intake includes two more wells SW-1 and SW-2 with a capacity of 40 m 3 /h, but they serve as a reserve. According to the water law permit, water intake may not exceed: Qhmax = 37.64 m 3 /h; Qdmax = 903.23 m 3 /d. Raw water taken from the source-deep wells, is directed to the building of the hydrophore plant where it is subjected to a onestage iron and aeration process. A central mixer is located on the iron remover, which results in an equal level of iron oxide precipitation. There are 5 pumps installed at the station, two of which are in operation all the time, and the rest of them serve as support. Thanks to this, the water from the equalizing tanks is directed to the water supply network. In the case of floating control, the pumps are usually switched on via a frequency converter, and the speed of the pump controlled by the converter depends on the pressure measured in the discharge manifold. In this way, the frequency converter guarantees the stabilization of the pressure in the water supply at the assumed level.

Research methodology
The basis for conducting the presented computer simulations was to reflect the natural operation of the water distribution system, and above all, the need to examine the behavior of the system with regard to any changes in the basic hydraulic parameters: flow rate and water pressure. The accuracy of the model was achieved thanks to the detailed knowledge of the water network and the reliability of the data collected from the exploitation. At the same time, it was assumed that the WDS works as a time-varying system.
The basis for the research was to create a model of the selected water supply network, in the Epanet computer program distributed by US EPA (Rossmann 2000), which was used as the basic tool for conducting various simulations. It should be noted that many paid applications for numerical simulations of water supply network hydraulics use the calculation algorithms contained in the Epanet program. The digital foundation of the water supply network of the village of Kleosin was used in the work. The materials were obtained from the GEOPORTAL website and contain the designation of basic elements of the water supply network, i.e., water supply sections, diameters, and lengths. In addition, the portal allows you to map street names, location of buildings, plot boundaries, and their numbers. The figure (Fig. 2) presents fragments of the Kleosin map, downloaded from the GEOPORTAL website (Trębicka 2018a, b).
The first step when creating a model of a water supply network with the Epanet program involved the introduction of the town map into the program, which was used as a foundation. Using the available computer application tools, a model was created that consisted of pump, tank, nodes, and sections.
Calibration of the hydraulic model was performed on the basis of pressure measurements taken simultaneously at various points in the network and data collected from telemetry. Thanks to this, it was possible to verify the observed results and apply the necessary corrections to the model (verification of pipe diameters, roughness, and the condition of the valves). An additional parameter confirming the correctness of the obtained results is the chemical composition of water at various points in the network, which corresponds to the results of monthly laboratory tests carried out for the needs. (Zimoch and Paciej 2018;Zimoch and Bartkiewicz 2018b). Each of the applied elements has been assigned technical parameters such as land elevation, length, water demand, location relative to the type of building, diameter, and roughness of the water pipe.
The next step in building the WDS (Water Distribution System) model was the need to specify for each node one of three categories: single-family housing areas, multi-family housing areas, and industrial areas. Each of the categories has different water partitioning values over time. The obtained data were assigned to specific nodes, added up, and entered into the program.
Using the available tools of the computer application, a model was created, which consisted of pump, reservoir, nodes, and sections.
Each of the plotted elements has been assigned technical parameters such as land elevation, length, water demand, location in relation to the type of development, diameter, and roughness of the pipes.
Data on water consumption, obtained in the Enterprise of the Voivodship Board of Melioration and Water Facilities in Bialystok in the form of annual water consumption, were averaged and converted into the average daily consumption in m 3 /d.
To compile data on the efficiency of the water supply network, it was necessary to define our own methods of collecting and processing all information on actual water consumption. In order to meet these conditions, which are the basis for the mapping of the water supply network, modern digital maps were used. Computer simulations, on the other hand, were carried out using the Epanet program, so often recommended in scientific circles and used in various types of practical applications, where quick diagnosis is necessary.
The network model consists of one tank (1), which is the node representing the source of the network, one pump (1), described by the number of the node in which it is located, 64 numbered water pipes that carry water from one network point to another, 42 nodes that represent points in the network where connections meet or where water flows in or out of the network. The diameters of the pipes range from 90 to 225 mm, the largest share is that of 110 mm in diameter-approx. 60%, and the smallest of 160.00 mm-1.59%. The maximum hourly demand is 50.95 m 3 /h and the average is 46.31 m 3 /h.
Each of these objects has been assigned specific values. The nodes were assigned land elevation and water partitioning, water pipe diameters and lengths and hydraulic height and pressure for the tank. In the case of a pumping station, which is defined by the number of the node in which it is located, the number of installed pumping units and six values characterizing the capacity, pressure, and efficiency of one pumping unit (including extreme and nominal values) is given.
Thanks to this, it was possible to simulate the water supply network model in the Epanet program and obtain parameters characterizing the entire network, i.e., flows (m 3 /s), flow velocities (m/s), pressure in nodes, friction coefficients, and unit loss coefficients (m/km) for the calculation, which was used by the Hazen-Williams formula (Trębicka 2018a, b). In the study, the Hazen-Williams formula is chosen due to the fact that it is considered one of the most popular pressure loss equations for distribution systems, which is reflected in numerous publications and scientific studies. In the Hazen-Williams formula, the linear loss coefficients are calculated according to the formula (1) (Rossmam 2000): where

C-Hazen-Williams roughness coefficient [-], d-pipe diameter [mm], L-pipe length [m].
In the Hazen-Williams formula, the value of the n coefficient is 1.852.
The formula uses the following equation to calculate the pressure drop between the start and end nodes of a pipe (2) (Rossmam 2000): where: ℎ L = headloss (Length), A = flow rate (Volume/Time), q = resistance coefficient, and B = flow exponent.
The above figure (Fig. 3) shows a diagram of the water supply network of the town of Kleosin, with the numbers of nodes and sections marked, as well as the source from which water is taken to cover the demand.
In the research part of the work, the water supply network was simulated in different variants of work. The basis was the reconstruction of the hydraulic system of the water supply network, in its existing state, which is the basis for further research and measurements. The following changes of individual system parameters were compared to the steady state (state without noticeable changes in the network). Based on the results obtained, it was possible to carry out a thorough analysis. As part of this work, a proposed attempt to add an additional tank near the main water intake is presented.
All the applied variants were simulated in various operating conditions: fire occurrence and operation during the greatest and lowest water consumption in the network. In (2) h L = Aq B the simulation process, in the created model, a number of situational variants were analyzed, where the starting point was always the steady state, i.e., the existing system.
The article includes the SYM_M variant, which is a modification of the existing real water supply model by adding additional elements (i.e., nodes, sections due to the planned expansion), aimed at improving the operation of the network. It should be noted that the objectives of the modernization process were to improve the existing working conditions of the WDS, as well as expansion due to area demand.

Results and discussion
Behind it, the model was subjected to simulation tests, the failure-free operation of the water supply network was mapped, thus defining the steady state, as a result of which the results were averaged over a day (Fig. 3). The average daily demand for water is 821.11 m 3 /d. The highest volumes of water in the network were observed at 8.00-55.97 m 3 /h and the lowest at 23.00-9.73 m 3 /h.
There are no nodes in the network model where there would be no water demand. The water supply network is mostly made of PVC pipes, so the roughness coefficient was assumed to be 140 (Table 1). In the simulation variant, for the purpose of checking the operation of the network in terms of the required pressures, the total simulation time was assumed to be 24 h. To check the residence time of the water in the network, the simulation time was set to 240 h, as recommended by the US Environmental Protection Agency (US EPA). However, the characteristics of the pumps in the simulation variant were introduced based on the manufacturer's data. Hourly variability of the water demand was described by means of the presented graph. (Fig. 4).

Model of the modernization process of the water distribution system
In the variant marked as the simulation of the SYM_M system operation, an attempt was made to upgrade the planned modernization. In this variant, an attempt was made to optimize the operation of the water supply network by changing the model shown in Fig

Simulation of network operation at the time of greatest demand for water
The pipes in the model have diameters from 90 to 250 mm. The average daily water flow in the pipes is 69.85 m 3 /d. The average speed in the pipes is 0.05 m/s, while the average pressure in the network is 40.19 m. The computer model of  the water supply network was simulated at the hour of the highest and the lowest consumption of water.
The highest value of pressure at the hour of the water consumption was recorded in node No. 13 and amounts to 37.18 m, while the minimum value in node No. 40 is 21.26 m. The results turned out to be very similar to those obtained when reflecting the steady state. Figure 6 illustrates the distribution of pressure in the nodes in the water supply network at the time of the highest consumption.
During the simulation of the network at the hour of the lowest water consumption, the pressure with the highest value was recorded at node 13 (56.73 m) and the lowest at node 40 (40.73 m). Figure 7 illustrates the distribution of pressure in the nodes in the water supply network at the time of the lowest consumption.   Figure 8 shows the pressure profile that prevails in the nodes included in the main pipe.
The model was simulated in the event of a fire in the same way as in variant No. 1. At the hour of the highest and lowest water consumption, in node no. 40, the demand for water was increased by a hypothetical fire expenditure of 15 l/s (1296 m 3 /d) (Ordinance of the Minister of Interior and Administration of July 24, 2009, on fire-fighting water supply and fire roads). The node with the lowest water pressure was assumed as the location of the fire. Figure 9 illustrates the pressure distribution throughout the network.
The flow with the highest value, observed during the network simulation, took place in pipe no. 1 and reached the value of 47.48 m 3 /h. The lowest value, equal to 0.025 m 3 /h, occurs in section no. 42. Both the highest and the lowest value increased in comparison with the variant representing the existing state. Figure 10 shows the pressure profile that prevails in the nodes included in the main pipe.
The highest flow velocity took place in pipe no. 1 and reached 0.27 m/s, on the other hand, a speed of 0 m/s was observed in three pipes numbered 9, 14, and 42 at the hour of highest consumption (8.00). Referring to the variant representing the steady state, in the pipe 58, the speed improved from 0 m/s to 0.1 m/s. This fact, due to the results obtained, has been subjected to special observation and analysis, it is probably related to the oversizing of the network, which is a problem for small towns in Poland, and at the same time the result of a systematic decrease in water consumption in the city's distribution systems. Currently, research is carried out to diagnose the situation, and the conclusions will be published in subsequent articles. Figures 11 and 12 show water velocity in the water supply network at the time of the highest consumption and the lowest consumption.
After simulating the operation of the water supply network of the town of Kleosin and analyzing the obtained results, a number of important and significant determinations of behavior in the operational reality under given conditions were made. The values of the water flow velocity in the network, regardless of the variant, are too low. In most pipes, the average achieved speed does not exceed 0.11 m/s, and many of them have values close to water stagnationthe speed is less than 0.1 m/s. This necessitates periodic flushing of the conduits. The recommended optimal speed for pipes with a diameter of up to 300 mm is in the range of 0.5-0.8 m/s. The reason for this situation is the restrictive fire protection standards that had to be met by the waterworks built in the past, which caused today's waterworks of this type to be oversized. Time may be a solution to the problem, as the flow velocities increase with the increase in flow, and the water intake in the analyzed network is higher from year to year. The minimum value of the pressure must guarantee comfort of consumption acceptable to the user, and the maximum value must meet the requirements of safe operation. The average pressure values in each of the analyzed variants are in the range of 26.07 -40.22 m. This ensures that all users are supplied with water under the appropriate pressure. An attempt was made to improve the functioning of the water supply network. New nodes and lines have been added, and the diameter of existing lines has also been changed. The effects of such modernization turned out to be counterproductive, that is, it failed to improve the functioning of the water supply system. The average speed in the system dropped to 0.05 m/s and the flow value decreased Fig. 9 The pressure distribution in the model of the water distribution system at the hour of the highest water consumption Fig. 10 Pressure profile in the nodes of the main trunk line at the hour of the highest consumption by about 7%. An additional negative factor was the cost of the network modernization and increased financial outlays for the functioning of the water distribution system. The only positive aspects include increasing the reliability of the tested network.

Conclusions
The paper presents a computer model of water system management and simulation in various operating conditions with the use of the Epanet program. The creation of a computer model mapping the layout and operation of the water supply network required the use of a digital Kleosin map, which was used in the computer application as a basis for further work.
The use of computer modeling of the water network, conducting simulations in various conditions of use, makes the analysis of the obtained results much easier. With proper and skillful use of the program, Epanet appears as a powerful analytical tool, which makes solving problems related to the water supply network much simpler and less risky, including minimizing the impact of failures on the operation of the rest of the system, or making decisions on planned projects and modernizations.
Through the simulation process, it becomes possible to forecast issues and ensure that the water supply meets both sanitary and quality requirements. This purpose can be achieved by building a model of the water supply network and carrying out the most convenient situational variants. It is an excellent tool that allows extending the reliability calculation in the context of the assessment of the probability of an event and the assessment of the hydraulic effects of the planned modernization.
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Fig. 11
Water velocity in the water supply network at the time of the highest consumption Fig. 12 Water velocity in the water supply network at the time of the lowest consumption