Verifying an improved intermittent water distribution network analysis method based on EPA-SWMM

Water distribution networks (WDNs) are designed to provide reliable, safe, and adequate water to users on a continuous basis to satisfy their needs throughout the day. A lack of water resources coupled with economic and political factors resulting in a lack of investment in infrastructure can prevent water distribution systems from operating according to their design purpose, as seen in examples such as Zambia (Simukonda et al. 2018), South Africa and Sri Lanka (Charalambous et al. 2016). WDNs that provide water to customers less than 24 h a day are termed intermittent water supply (IWS) systems, affecting nearly one-third of all piped water users worldwide (Kumpel & Nelson 2016; McIntosh 2003).

The typical operation of IWS systems involves the partition of the entire network into different zones based on the number of customers and then allocating a proportion of the available limited water to each zone for a fixed period of time, which is usually less than 24 hours (De Marchis et al. 2011). Customers attempt to manage the sporadic water service by utilizing household tanks (Criminisi et al. 2009). The intermittent operation of a WDN leads to network filling and emptying processes during which both free surface and pressurized flow conditions occur in network pipes (Batish 2003; De Marchis et al. 2010).

Various methods have been proposed for accurate simulation of IWS systems, with many relying on the conventional hydraulic analysis tool, EPANET (Sarisen et al. 2022). However, under the assumptions of pressurized pipes, and steady and incompressible flow, EPANET falls short of representing IWS systems in an entirely accurate manner; yet it has been utilized by some researchers with different methods to address the issue of inequitable supply problem (Ameyaw et al. 2013; Freni et al. 2014; Gottipati & Nanduri 2014). Including the network charging and emptying processes in the analysis can lead to more precise modelling of IWS systems. This will consider the time when each consumption node begins receiving water, which is critical in addressing the unequal distribution of water among consumers (Sarisen et al. 2022).

Experimental investigations were performed to validate numerical models concerning the pipe-filling process; rigid water column (RWC) models (Liou & Hunt 1996; Hou et al. 2014; Coronado-Hernández et al. 2017), elastic water column (EWC) models (Zhou et al. 2011; Zhou et al. 2019) and computational fluid dynamics (CFD) models (Besharat et al. 2018; Paternina-Verona et al. 2023). All the models used have acceptable accuracy and limitations depending on the conditions applied. Additional information regarding the studies conducted and their models can be found in Fuertes-Miquel et al. (2019). The experimental setups that have been used mainly involve individual pipes or pipelines of undulating profiles. The models that have been used require a lot of time and computational resources, rendering them unsuitable for conventional engineering practices concerning water networks (Ferreira et al. 2023).

EPA's Storm Water Management Model (EPA-SWMM), renowned for its capability to simulate both free surface and pressurized conditions (Rossman 2015), is widely recognized as a suitable tool for the simulation of IWS systems. Its utility has been demonstrated through various approaches adopted by several researchers (Segura 2006; Cabrera-Bejar & Tzatchkov 2009; Kabaasha 2012; Shrestha & Buchberger 2012; Dubasik 2017; Campisano et al. 2019b, 2019a). Among all these methods, only Campisano et al. (2019a) validated their approach for the ability of EPA-SWMM to represent the behaviour of the network filling process, using a field experiment conducted in a WDN in Sicily (Italy). However, they used Wagner et al.'s (1988) equation to implement the pressure dependency of the flow rate. This equation has a threshold flow rate equal to the average flow rate (demand) corresponding to the required pressure in the system. Above the required pressure, the flow rate remains the same (equivalent to the demand). The pressure dependency of the flow equation with an upper limit on the flow rate (controlled-type demand representation) applies only to WDNs with sufficiently long supply duration (Mohan & Abhijith 2020). In this study, the orifice equation was seen to be suitable for simulating uncontrolled-type demand, which was justified by Reddy & Elango (1989) and was recommended by Vairavamoorthy (1994) and Mohan & Abhijith (2020). No consideration was given to the air pressurization process during the pipe-filling events as the current version of EPA-SWMM does not account for this process. However, an AirSWMM model was recently developed by Ferreira et al. (2023) with the integration of a conventional accumulator model in the existing EPA-SWMM's source code. By comparing the EPA-SWMM model to the AirSWMM model and experimental results, they found that EPA-SWMM accurately simulates the pipe-filling behaviour in terms of pressure heads when using a larger orifice (21 mm) configuration in a simple experimental study. Given the lack of suitable software available to accurately describe air behaviour in free surface flow models for closed pipes (Ferreira et al. 2023), this study aims to demonstrate that the improved EPA-SWMM model proposed in this study provides reasonable results for simulating IWS systems based on experimental data. This study holds significant importance as it delves into a relatively unexplored area. To date, only a handful of studies have centred on IWS, particularly with a focus on experimental work (Chinnusamy et al. 2018; Ferrante et al. 2022; Weston et al. 2022).

The contributions of this paper include (a) presenting an improved EPA-SWMM model for simulating IWS systems under different conditions; (b) introducing a method for determining outlet coefficients, which addresses the challenges associated with acquiring calibration data for an IWS model; (c) integrating Genetic Algorithm (GA) (optimization) with EPA-SWMM for the IWS model calibration.

The paper is structured as follows: Section 2 explains the proposed method and justifies the modelling of IWS systems with the uncontrolled type of outlet. A description of the experimental work conducted on a laboratory-scale water distribution network is provided in the following section (Section 3), which includes laboratory set-up and data acquisition procedures. A brief overview of the EPA-SWMM model is presented along with its application to the experimental WDN, followed by the calibration and validation procedure. Section 3 also analyses the performance of the EPA-SWMM model against experimental data. And further verifies the model's applicability to real-world IWS. Section 4 details the software used and provides information on data availability. Finally, in the final section, conclusions are drawn.

Equation (2) was embedded in the outlet link to assign pressure dependency of flow. Control rules were used to set the status of the dummy pipes to be closed to introduce the float valve behaviour at each equivalent tank.

Another outlet element was connected to each tank to represent the water consumption from the household tanks during supply and non-supply hours. The proposed method employs the household tanks filling at a pressure-dependent rate and emptying based on the user's water consumption from the tank. Other model settings, such as the source representation and features of junction nodes, are the same as those of Campisano et al. (2019b).

Due to the complexity of real water distribution systems and uncertainties in service pipe connections and leakage, determining the outlet coefficients (K_i) and leakage coefficients (C_i) for each individual node is a highly challenging task. In this study, an alternative approach was suggested to approximate the K_i and C_i values depending on the expected demands and the leakage rate at nodes. This method involves considering the initial demands at nodes and utilizing the simulation results (nodal pressure) obtained from EPA-SWMM demand-driven analysis (DDA) as suggested by Kabaasha (2012). In his method, demands were introduced to junction nodes as negative inflow and no other artificial elements were connected to the junction nodes (Kabaasha 2012).

The proposed nodal configuration approach was then implemented into an EPA-SWMM-based network simulation. This configuration helps in resolving the pressure dependency of the flow when the number of households (served by a network) are aggregated to a node. Additionally, the proposed method takes into account leakage, which is a significant issue in IWS systems.

For a specific cross-sectional geometry, the flow area A is a known function of water depth Y which in turn can be obtained from the head H.

Each ‘node assembly’ consists of the node itself and half the length of each link connected to it (Rossman 2017). The equations (Equations (3), (4) and (6)) are solved by the chosen dynamic wave analysis option as it generates the most theoretically accurate results and can account for channel storage, backwater effects, and pressurized flow. The implicit backwards Euler method is used to solve the spatial and temporal derivatives in Equations (4) and (6) to provide improved stability.

The method (Figure 1) was initially applied to a lab-based, simple experimental network with the objective of testing if it works hydraulically. The model application strategy included the calibration of minor loss coefficients and pipe roughness coefficients for the laboratory-based experimental network. The calibration performance was quantified using four statistical measures. These are Root Mean Square Error (RMSE), Median Absolute Percentage Error (MDAPE), Coefficient of Determination (R²)/Nash-Sutcliffe Efficiency (NSE), and Pearson correlation coefficient (PCC). Utilizing multiple metrics is intended to offset the limitations of each individual metric when evaluating the performance of the model.

Lower values of RMSE and MDAPE indicate a better fit of the model, while higher values of NSE and PCC (Equation (10)) represent better model performance.

In Experiment 1, the reservoir was situated 1.46 m above the ground. The outflow orifice, which refers to the invert of the outflow pipe, was placed at an elevation of 1.5 m. A 50.8 millimetres (mm) diameter ball valve was installed in the outflow orifice and kept fully open throughout all three experiments. To prevent water from spilling over, an overflow orifice was positioned 2.00 m above the ground (Figure 2(a)). The maximum head of the reservoir was approximately 2.2 m. For Experiment 2, the reservoir elevation was lowered to 0.96 m, resulting in the invert of the outflow orifice elevation of 1.00 m and a maximum head of approximately 1.7 m. To determine the reservoir volume, the outer surface of the barrel was marked with an increment corresponding to the 18.92 l (5 gallons) volume.

The distribution network consists of 21 PVC pipes with a total length of 25.76 m. The network includes two sections of 50.80 mm (2.00 inch) diameter pipes, a single 38.1 mm (1.50 inch) diameter section, and 18 sections of 25.4 mm (1.00 inch) diameter pipes corresponding to DN values of 50, 40, and 25, respectively. The PVC was Schedule 40, so rated up to 450 psi pressure. There are 18 nodes, of which 14 are junction nodes where the pipes are connected. Four are referred to as demand nodes at which water discharges from the network into collection bins, as shown in Figure 2(d). The demand nodes were installed with 1 inch full port PVC ball valves (DN 25) that simulate taps. Discharges from each demand node were directed into collection bins through a 22.5 degree elbow connected to a short length of 1 inch PVC (Figure 2(d)). Junctions where the pipe diameter decreases were fitted with adaptors. Differences in elevation between adjacent nodes necessitated the installation of a flexible rubber conduit modified from a commercial automobile radiator hose (Figure 2(b)). All nodes were elevated to a particular height using specially constructed stands that allow the height to be adjusted (Figure 2(a)). No stand was required for Node 22 since it discharges at the floor level (Figure 2(c)).

The volume of discharge from each demand node was measured by using translucent storage bins with a capacity of 99.4 l (26.3 gallons) with height markings corresponding to 3.78 l (1.00 gallon) increments. The volume accuracy of the collecting bins for the outlet discharge was ±1.89 l (a half gallon). The accuracy of the flow rate then depends on the time of collection, which was accurate to 0.1 s. The lowest node, Node 22 (Figure 3), was designed to discharge into a drainage trough at floor level. To measure the discharge for Node 22, a section of the trough (1.83 m or 6.00 feet long) was modified with two polystyrene foam ‘gates’ at both ends. Instead of volumetric increments, water level heights in 6.35 mm (0.25 inch) increments from the bottom of the trough were noted on the lower gate. A hole was drilled through the bottom left corner of the lower gate to release water after the trial was completed. The hole was sealed with removable plumbers' putty to prevent leakage during the trial (Figure 2(e)).

Video equipment was used to record the filling of each translucent bin in each trial and the time at which water begins and ceases to flow at each demand node (Figure 2(c)). Four commercial digital cameras and a mobile phone were placed on a tripod or nearby ledges to record flows at the four demand nodes. A mobile phone camera placed in front of the reservoir also captured the falling water level in the translucent barrel.

Experiments were conducted to simulate the situation where customers leave their taps open and collect as much water as possible.

• Experiment 1: The falling-head reservoir scenario with different reservoir and distribution system characteristics was examined, as explained in Section 3.1.1.

• Experiment 2: The falling-head scenario was repeated in the second experiment, but the source and nodal elevations were adjusted as described in Section 3.1.1. Table 2 provides a summary of the experimental set-up.

At least three trials were performed for each experiment. Video recordings were then used to identify the precise timing and duration of the flow rate at each demand node. This information was then combined with the volume measured in the corresponding bin or trough to calculate the average flow rate at each demand node. The videos of the demand nodes were also examined to create outflow hydrographs. By measuring the filling time between 3.78 l increments marked on the collection bins, time-varying flow rates were estimated. Finally, recording of the falling reservoir level allowed an average outflow rate to be calculated and the outflow hydrograph to be generated.

The calibration of the model was formulated as an optimization problem using a GA. For this purpose, a Python code was written using the Platypus module (Hadka 2016) for GA, combined with the SWMM-toolkit as detailed in Section 4. GA is an efficient optimization tool commonly used to address WDN optimization problems (Javadi et al. 2005; Martínez et al. 2007; Tabesha et al. 2011; Jung et al. 2016).

Time series of flow rates recorded for each demand node and reservoir in the experimental study were used as observed data for the calibration of the model. RMSE (Equation (7)) was found appropriate for the objective function after conducting the calibration using other statistical parameters (i.e., MDAPE (Equation (8)) and NSE (Equation (9))) as the objective function.

The function evaluation procedure includes the following steps, as shown in Figure 5(b): The EPA-SWMM model is configured with updated minor loss and Manning's coefficients. Simulation is then executed in EPA-SWMM, and the results of the time series of inflow for each demand node and outflow from the reservoir are generated. These results are then compared with observed data, and RMSE (Equation (7)) is calculated.

In order to find the global optimum, parameter tuning was carried out for the GA algorithm. For these reasons, before initiating the calibration and validation process, GA parameters were determined with several tests. The following parameter combinations were chosen for the calibration and validation procedure: Population size (PS) is 40, probability of Simulated Binary Crossover (SBX) (P_c) is 0.9, probability of Polynomial Mutation (P_m) is 0.05, and distribution indices (DI_m and DI_c) are 20. The number of the evaluation function was kept at 10,000.

A time step of 1 s, based on the small length of pipes, was used. Minor losses at junctions were considered and both minor loss coefficients and Manning's pipe roughness coefficients were calibrated with a GA also considering the values recommended in the literature (The Engineering Toolbox 2004; Frost 2006; Brawn et al. 2009; VDOT 2021) and using engineering judgment. In Experiment 1, minor loss coefficients and Manning's roughness coefficients were calibrated simultaneously with the experimental data (time series of flow rates at demand nodes and water level at the source). The Manning's roughness coefficients determined after the calibration of Experiment 1 remained unchanged in Experiment 2. Due to modifications in junction elevation, minor loss coefficients for Experiment 2 were recalibrated.

It should be noted that although the models were calibrated and validated with a small-scale network, the time series of inflows at all demand nodes and the time series of outflow from the storage tank (source) were used for calibration and validation. This increases the accuracy of the calibration but makes it more challenging to reproduce the same model results with experimental data.

The impact of the pipe-filling process and hence uncertain transient flow conditions is high in this experimental work as the duration is short. When the valve connected to the source (barrel) is opened, the network pipelines are progressively filled with water with the values of the flow characteristics, velocity, pressure, and positions along the pipeline changing with time until steady state conditions are established (Figure 6). As it can be seen from Figure 6, there is a similar flow pattern at each node across the two experiments where outflow varies in high rates at the beginning of the filling process and drops sharply to steadier outflows. While the flow rate in C1 is well captured by the model, the model has difficulty capturing the high flow rate occurrence at nodes at the beginning of the simulation (Figure 6). One explanation from the perspective of modelling might be the air presence in the network, which EPA-SWMM does not take into account. During the filling stage, water rapidly enters the system, causing the release of trapped air. This release of air impacts the flow rate entering the system, thereby delaying pipe filling and affecting the time it takes for water to reach the nodes that are open (Ferreira et al. 2024). When water enters an empty line, it will accelerate in reaction to the driving head, and friction will modify this acceleration. The presence of air initially offers minimal resistance. However, as the approaching waterfront reaches the outlets, compression of residual air within downstream segments occurs, leading to a significant deceleration in flow, particularly at critical nodes that are open. This phenomenon results in the observed sharp decrease in flow rates, as shown in Figure 6.

To investigate the practical application of the proposed method, it was implemented on a real-case IWS network acquired from the existing literature (Campisano et al. 2019b). This network is responsible for the distribution of water to a district within the Ragalna municipality, located in the south-eastern region of Sicily, Italy. The network, operating on a gravity-fed system, is equipped with a constant head tank of 2.8 m, facilitating water supply to 56 nodes via a network of 58 pipes. Its daily demand totals around 1,151 m³ per day. In their study, the researchers conducted a field investigation specifically targeting the filling phase of the network. They employed an ultrasonic flowmeter installed at the source outlet to gather flow measurements, which were then used to estimate the demand values. Furthermore, pressure data were obtained from two pressure gauges located near Nodes 13 and 46, with measurements taken at 5-min intervals. The network was empty at the beginning of the simulation, which lasted 4 h. More detailed information regarding the network data and nodal demands can be found in the work by Campisano et al. (2019b).

The pressure values for each node were obtained from the simulation results and employed in Equations (1) and (2) (Section 2) to compute the C_i and K_i values for each node. In this case study Q_L,i was assumed to be 15% of initial nodal demand and Q_i was 85% of initial nodal demand.

To assess the accuracy of the model, time series data of pressure values were obtained from the EPA-SWMM simulation results for Node 13 and Node 46 and compared with the corresponding field data. Notably, these are the two nodes for which time series of pressure data from the field were provided in Campisano et al. (2019b). The field data were extracted from the figure presented in Campisano et al. (2019b) using the web-based tool ‘WebPlotDigitizer’ (Version 4.5; Rohatgi, 2021).

The application of EPA-SWMM to a real case study made it possible to further validate the model results against the field data.

In terms of computational time, both experimental simulations and real-case simulations were evaluated, with the computational time required by each case depicted in Table 6. The experimental network, comprising 21 pipes and 18 nodes with short-length pipes, was executed in less than 1 s, while the real-case study, featuring 58 pipes and 56 nodes, took 1 s to complete the simulation (Table 6). The relatively low computational time required to run the model is largely attributable to the shorter simulation duration. Therefore, it is not expected that computational time for larger networks will be excessively long. Factors such as network size, model complexity, and simulation parameters significantly impact computational requirements. However, compared to EPANET-based IWS modelling approaches, EPA-SWMM-based models take longer due to the intricate calculations involved. For instance, for the same network (real case study) and simulation duration, EPANET-based IWS modelling approaches were executed in less than a second (Abdelazeem & Meyer 2024).

EPA-SWMM version 5.1 was employed for modelling tasks, with Python facilitating interaction through the SWMM-toolkit 0.9.0 module. For optimization, the Platypus-Opt module version 1.0.4 was utilized. Python scripts for calibration, data gathered from experiments, and input files for both the experimental IWS network and the real case study are publicly accessible on Mendeley Data (Sarisen et al. 2023).

The scarcity of real-world data compounds the challenge of accurately replicating and validating the behaviour of these systems. Notably, to the best of the authors ‘knowledge, no experimental study has comprehensively replicated the complete behaviour of an IWS system to verify model accuracy. There exists no IWS modelling approach that has undergone validation with a real-world case study encompassing user behaviour, household tanks, and system leakage.

This paper addresses these gaps by conducting a series of experiments on a laboratory-scale IWS set-up, capturing flow rate data under various conditions from all demand nodes. A model based on EPA-SWMM was formulated to simulate uncontrolled outlets. Utilizing GAs integrated into EPA-SWMM, minor loss coefficients and pipe roughness coefficients were calibrated for the first time. The EPA-SWMM model, validated through experimentation, was further refined to incorporate pressure dependency of flow rates, considering service connections and the associated minor losses. In pursuit of this objective, the orifice equation was seamlessly integrated into an artificial outlet element, establishing a connection to each node. Leakage was similarly simulated using the orifice equation, applied individually at each node. Both leakage and outlet coefficients were recommended to be determined via the DDA within the EPA-SWMM, utilizing nodal pressure outputs. To demonstrate the potential of our proposed method in analyzing various IWS-related issues (such as inequitable water supply) and enhancing the level of service (for instance, transitioning to continuous water supply) in real-world IWS systems, the proposed method was further validated using a real case study documented in the existing literature. This further substantiates the efficacy and applicability of the approach. Drawing from the analysis and the attained outcomes, the subsequent conclusions were derived:

• While the experimental models successfully captured source outflow rates, achieving precise replication of flow rate fluctuations at individual nodes posed challenges. Potential contributing factors encompass inaccuracies in manual flow rate measurements, water losses between the reservoir and collection bins, and the presence of air within the network. Subsequent investigations could be directed towards a larger-scale IWS system fitted with pressure and flow sensors, affording more frequent and dependable data acquisition, thus mitigating these sources of error.

• In the context of small-scale IWS systems, it is essential to recognize the significance of minor loss coefficients and prioritize the refinement of calibration techniques. This could involve more comprehensive datasets and refining algorithm parameters.

• The orifice equation seems suitable for establishing the pressure-flow relationship necessary to emulate uncontrolled outlets as found in IWS systems.

• Considering the notable prevalence of leakage in IWS systems, the leakage component's inclusion in modelling IWS should not be disregarded.

• Given the complexity and uncertainties of the service pipe connections, the prediction of outlet coefficients through the DDA method in EPA-SWMM is promising.

• The proposed IWS modelling method presents a versatile tool for various applications, including design, scenario analysis, and management of IWS systems. Its utilization extends to addressing critical issues within these systems, particularly inequitable water distribution. Built upon EPA-SWMM, the method enhances accessibility as it is open-source and freely available for adoption by water utilities. Moreover, its potential applications in decision-making processes are extensive, ranging from optimizing water allocation strategies to identifying vulnerabilities in the water supply system.

• The proposed method may not be applicable to systems where suction pumps are prevalent.

• To ensure effective implementation, the research underscores the importance of comprehensive data collection, particularly regarding consumer connections and coping strategies. This data, including details on the number of connections and consumer behaviour under various conditions, forms a crucial foundation for accurate modelling and informed decision-making within IWS management.

• The validation of the improved IWS modelling method is limited to the pressure data set spanning 4 h, with assumptions made regarding the number of connections based on given demand data. Further validation of the proposed method could be done by using another case study, utilizing the aforementioned comprehensive dataset.

The authors thank R. Fritz of Michigan Technological University for assistance with the construction of the laboratory-scale system and implementing the experimental procedures. The editors and anonymous reviewers of the paper are gratefully acknowledged by the authors for their insightful comments on the paper.

This work was supported by the Republic of Türkiye Ministry of National Education.

All relevant data are available in Sarisen et al. (2023). Data can be found at https://data.mendeley.com/datasets/dhk3p4y6b9/1.

The authors declare there is no conflict.