Equity analysis of intermittent water supply systems by means of EPA-SWMM Open Access

Over 1 billion people worldwide are affected by intermittent water supply (IWS) systems (Kumpel et al. 2022). IWS is known as a water supply that provides customers for a period shorter than 24 h per day or a couple of days per week (Rawas et al. 2020). It is caused by a combination of a number of factors, population growth, water shortage, leakage, insufficient vision and planning, and fast demand growth as a result of urbanization (Klingel 2012; Laspidou et al. 2017). Farmani et al. (2021) also identify infrastructural limitations and water resources availability as major causes of IWS in most supply networks, with power outages being the primary external factor. However, among these factors, leakage is pointed out as the main and most common reason behind IWS (Laspidou et al. 2017).

These factors cause water supply networks, which are normally designed assuming continuous supply, to operate as an IWS system, which causes several negative impacts on utilities, customers, and the community, such as: reduced distribution equity, accelerated degradation of the network, monetary burden on customers, decay of the water quality, and deterioration of community health (Fontanazza et al. 2007; Klingel 2012; Bivins et al. 2017; Burt et al. 2018). Even networks that operate in continuous supply can have supply disruptions whether due to intentional or unexpected interventions. Although these disruptions are often one-time events, their effects are remarkably similar to those of IWS (Preciado et al. 2021). The term equity includes the preservation of water rights and access to clean and safe water for drinking (Phansalkar 2007). Ameyaw et al. (2013) also defined equity in the distribution network as the supply of an adequate amount of water for consumers across the network.

According to De Marchis et al. (2010) and Manohar & Kumar (2014), the network topology, topography, supply area, and the use of overdesigned private tanks are relevant factors for water inequity during distribution; consequently, the competition for water increases among consumers. Under these conditions, consumers gather the maximum volume of water possible, depleting the limited available water quickly (Chandapillai et al. 2012). The effect of water scarcity in the system can be minimized if equity during the distribution is maximized (Chandapillai et al. 2012). Even in situations when the amount of water supplied would be sufficient to cover the consumers' demand, inequitable distribution of water is created by IWS that may involve up to a 200% dispersion (Fontanazza et al. 2007).

Several formulas to describe equity in water distribution systems are found in scientific literature, but the most important in recent contributions are: inequity equation by Chandapillai et al. (2012), which defines inequity as the highest disparity in supply and demand ratio at the moment when the demand of a single node in the network is met; deviation of equity equation by Ameyaw et al. (2013) that was proposed as an equation to minimize the discrepancy of water supplied to consumers nodes in comparison to the average supplied to all nodes; and uniformity coefficient (UC) equation by Gottipati & Nanduri (2014) is computed as the average ratio of the volume of water supplied at each node in the network to that of the demand variation of water at each node.

The impact of IWS operations in water distribution systems is not fully understood yet and there are no numerical modelling tools well-suited for the purpose. Furthermore, not much research has been carried out in the field of IWS before 2012, period in which, the majority of the existing publications only describe the causes and effects qualitatively but not quantitively (Klingel 2012; Zyoud 2022). Nevertheless, there has been significant growth in the number of publications in the field of IWS in the period post-2012, when 82.0% of total research publications in the period 1875 to 2021 were made (Zyoud 2022).

Standard water distribution modelling software, such as EPANET, assumes continuous pressurized flow. However, during the filling and emptying processes of IWS systems, the network operates not only in pressurized but also in free-surface (unpressurized) flow conditions, a situation that cannot be modelled by standard water distribution software. Alternatively, Campisano et al. (2018) proposed to use EPA-SWMM to model IWS systems. Even though the program was originally designed to model drainage networks, its ability to model both pressurized and unpressurized flows and respective transitions, enables a more realistic description of IWS.

During the network filling process, the pressure difference is quite significant due to the sudden pressure change, that may be assumed atmospheric at the frontline of water, thus the initial velocity of the frontline of water within an initially empty pipeline can be reasonably big (De Marchis et al. 2010). On the other hand, during the emptying of the network, pressure deficit and related partial flow regimes may occur on the pipelines. In addition, the emptying process causes residual flows that increase the volume of water received by the consumers located at the lowest elevations of the network (Mohan & Abhijith 2020).

This paper assesses the suitability of EPA-SWMM for the analysis of IWS systems with a special focus on the evaluation of equitable distribution. For this purpose, a new coefficient to quantify equity, hereby called volumetric coefficient (VC), is introduced and compared with current equity coefficients available in scientific literature. The coefficients are tested and compared for a range of standard pipe filling and emptying supply scenarios.

EPANET version 2.2 was used for the initial modelling of the water distribution networks, since this software was natively developed to model this type of system. After that, the networks were converted to a format compatible with EPA-SWMM through a converter developed in-house, further details will be provided later in the paper.

After the conversion, EPA-SWMM version 5.1 was used to analyse equity in intermittent water distribution systems. The choice of this software was due to its ability to simulate transient, partial flows and transitions from pressurized to free-surface flow. These types of hydraulic conditions are common in intermittent systems, especially during filling and emptying periods or in situations of low system pressure.

Using the software EPA-SWMM 5.1, simulations were performed on both synthetic networks for the critical phases of operation of an intermittent system: network filling and emptying. Equity was calculated for each network and the results were analysed and compared.

Dynamic wave routing was the selected EPA-SWMM solver and the routing time steps were respectively 10 and 5 s for the synthetic networks 1 and 2, according to Rossman (2015) recommendation, which states that a shorter routing time step is required for dynamic wave routing when compared to any of the other flow routings. The reporting time step in all simulations was set to 1 min.

To simulate the pipe filling and emptying operations in synthetic network 1, a set of control rules was created with the goal to activate the pump that connects the source to the distribution network only between 6 AM and 2 PM. The intermittency in synthetic network 2 was modelled by adding an orifice (ORI_RV_1) between the reservoir and the pipe connecting the distribution area and programme it through control rules to be opened only between 6 AM and 2 PM. The orifice acts therefore as an on-and-off flow control valve.

Due to the purpose for which they were developed, EPANET and EPA-SWMM have particularities that differentiate one software from the other. However, most elements of a distribution network data can be transferred from EPANET to EPA-SWMM without significant changes. The remaining data requires a higher level of manipulation, plus there is also the need to create new data for the model to run on the EPA-SWMM. In summary, the EPANET INP file is inserted in the converter (developed in-house using Python programming language) that manipulates the data in order to adapt them to the format used by EPA-SWMM; after that, the INP file compatible with EPA-SWMM is created. The converter was developed mainly following the information available in the EPA-SWMM and EPANET manuals (Rossman 2015; Rossman et al. 2020), and the recommendations of Kabaasha (2012) who developed a similar converter.

The most important aspects of the converter have been addressed below:

• In EPA-SWMM, junctions are modelled as manholes, which are structures that store water. To avoid overflow, a high value of MaxDepth (manhole depth starting from ground level) was used. In addition, a very small area value is given to these structures whereby the volume of water stored in these structures is insignificant.

• EPANET allows the addition of multiple demands to a node; however, in EPA-SWMM, it is only possible to add one demand to a node. Thus, if more than one base demand and demand pattern are added to a node, the converter assigns the value of −1 to base demand, calculates the actual demand of the node and creates a new demand pattern for the respective node.

• To avoid tank overflow in EPA-SWMM, the approach proposed by Kabaasha (2012) was adopted, which consists of adding an orifice to the pipe that feeds the tank. This orifice closes when the water level in the tank reaches a level close to the maximum. This system is controlled via a control curve and control rules.

• Since it is apparently only possible to close a pipe in EPA-SWMM through control rules. When a pipe is closed at the beginning of the simulation in EPANET, the converter creates control rules in order to change the status of this pipe in EPA-SWMM to closed.

• Apparently, there is no direct or simple way to convert the valves from EPANET to EPA-SWMM. Therefore, the converter does not convert the functionality of the valves. The valves are converted into orifices configured to be completely open, and as stated above, it is not functional, serving only to make the connections made by the valve.

• In EPA-SWMM, it is mandatory to add at least one outfall node in the network for dynamic wave flow routing. However, to prevent the outfall from interfering with the hydrodynamics of the grid, the technique proposed by Kabaasha (2012) consists of creating the outfall without connection to the grid and at an extremely high elevation; thus, ensuring that the water does not leave the system through it.

• The conversion of pumps from EPANET to EPA-SWMM consists of manipulating the pump curves. When the converter identifies Single-Point or Three-Point Curves, they are transformed into seven points that are used to create the pump curve in EPA-SWMM. In EPA-SWMM, it is not possible to assign an efficiency curve to pumps, so the converter excludes these types of curves.

Detailed procedures of the conversion from EPANET to EPA-SWMM along with the convertor tools are available in the MSc thesis by Ceita (2022), upon which, part of this research was based.

From the three formulas found in recent literature: inequity equation by (Chandapillai et al. 2012), deviation of equity (D_E) equation by Ameyaw et al. (2013), and UC equation by Gottipati & Nanduri (2014); deviation of equity (Equation (4)) was selected as the most-suited formula for hydraulic analyses carried out in EPA-SWMM. Additionally, a new formula is introduced, i.e. VC (Equation (5)), and results have been compared with the obtained from the deviation of equity coefficient. The reason to focus on these two formulas is because both can be used in situations where part of the network is empty, which is important for analysing equity during the filling and emptying phases.

If the demand is fully fulfilled at all junctions, then the supply ratio at all nodes is 1, and the UC will consequently equal to one. A UC value below 1 shows that the water quantity across nodes is not equitably distributed (Gottipati & Nanduri 2014).

With respect to inequity equation, it requires that the network hydraulics be modified, because Chandapillai et al. (2012) during the development of this formula considered that customers collect water in private tanks (in this case representing their water demand) and when the supply begins they withdraw the highest flow rate possible until the tank is full, in an uncontrolled way. Thus, adaptations must be made in the simulation such as removing the demand pattern values, adapting the demand of the nodes, and closing valves or cutting off the node supply when the demand of each node is fully satisfied; these changes are not desired for the type of analysis proposed in this research. Furthermore, regarding UC, it produces negative values when more than half of the nodes in the network are not supplied, becoming inadequate when used in the analysis of the filling and emptying phases.

From this equation, the maximum equity in the water distribution network is found when the equation is equal to zero (D_E = 0%), indicating that the water demand of the consumers is evenly met for all consumers (Q_S = Q_av).

In the present work, an adaptation is done in this equation to limit the maximum value of D_E, because, in its original form, the maximum value of D_E depends on the number of nodes in the network. On the other hand, in its adapted form, the maximum D_E is 50%, this allows for example to make comparisons between different networks, something that in its original form is not possible.

The VC, a novel equation developed in this research, assumes that every node in a network has a percentage share of the total supply of the source. The allocation percentage depends typically on the base demand and demand patterns. In intermittent situations, the share percentage varies from node to node; however, some nodes will receive a bigger share than others. Maximum equity is expected when all nodes have the same level of demand satisfaction, meaning that the ratio between supply and demand of all nodes in the network is equal. Therefore, the spatial distribution of water plays an important role in network equity. Nodal demand is, also, a relevant aspect of equity in the network that is normally not addressed by other equity equations. Therefore, nodes with bigger water demand have a greater influence on the equity of the network, because these nodes can represent a bigger concentration of people in the area. When the VC value is equal to 1, the network is in the most equitable situation, while the closer VC value is to 0 less equitable the network is.

The coefficient is determined by the ratio of the required demand and the actual supply ratio in each node. In EPANET modelling framework, the nodal demand at each node can be calculated by running demand-driven simulation, while the actual supply can be determined by running pressure-driven simulation. In EPA-SWMM, the nodal demand and actual supply of the model can be determined from the lateral inflow and the supply in each node, respectively.

VC considers that every node has an influence on each other and in the overall equity value of the network; therefore, it considers the surplus and deficient supply to the nodes. Nodes with surplus supply are the nodes in an advantageous situation and the difference of supply and demand ratio of these nodes are higher than 0. Thus, the nodes in a disadvantageous situation have a deficient supply when compared to the rest of the network, hence, their difference of supply and demand ratio is lower than 0. Because of the continuity principle, the volume of water that is oversupplied to the advantage nodes correlates to the volume of water that should be supplied to disadvantaged nodes. The nodes with a difference of supply and demand ratio equal to 0 are those that are neither being oversupplied nor undersupplied, consequently, they would settle on the line of equity, the red line in Figure 2.

Before modelling any IWS operation, simulations were launched using EPA-SWMM 5.1 for continuous pressurized supply. These simulations were used to validate EPA-SWMM 5.1 versus standard EPANET software and, additionally, they were used as a reference when presenting the results for IWS (Figures 4 and 6) under the label of ‘continuous supply simulation’. Then, filling and emptying operations were modelled in EPA-SWMM 5.1 for the two synthetic networks, in 24-h simulations. At the beginning of the simulations (0 AM), both networks were empty, then the supply is turned on at 6 AM, moment the filling operation starts, and the networks become full and remain like that until 2 PM, when the water supply is turned off, this starts emptying process of the networks, finally the networks remain empty until the end of the simulation. The analyses of filling and emptying operations focus on the moments when supply is turned on and off, respectively.

For a more straightforward analysis, the minimum pressure threshold was set to zero. Therefore, if there is water in the nodes, they will be supplied independently of the pressure. EPA-SWMM does not allow negative pressures; therefore, if water is reaching a node, it means that the pressure in this node is greater than 0.

Figure 3 illustrates the time lag for water reaching every node after the water supply to the network begins. As illustrated, in network 1, nodes a02, a03, and a05 are the first to be supplied, which happens at the moment when supply begins (at 6 AM); node a10 is the last node to be supplied, which takes 44 min to occur (at 6:44 AM). In network 2, nodes b02, b03, and b04 are the first to be supplied, which happens at the moment when supply begins (at 6 AM); on the other hand, the last node to be supplied is node b47, which happens 42 min afterwards (at 6:42 AM).

The ‘total inflow’ depicted in Figures 4 and 6 corresponds to an EPA-SWMM node variable that, according to Rossman (2015), is the sum of all flows entering the node. The higher values of total inflow in the nodes observed after the start of the supply (Figure 4) indicate the filling phase, which is a transient state characterized by a hydraulic grade line moving with the water front during the pipe filling.

The moment that the value of the total inflow in the nodes stabilizes was considered as the moment at which the network is totally filled, pressurized and starts performing under steady- or quasi-steady-state conditions. Therefore, network 1 takes around 1:05 h to be totally full and pressurized, whereas network 2 takes approximately 51 min. Despite the fact of being bigger than synthetic network 1, network 2 has a shorter filling time. This unexpected result can be associated with the fact that, contrary to network 1, network 2 is supplied by gravity; therefore, the flow is not limited by the pump's maximum flow but by the level of the source (reservoir S1). Pump l01 in network 1 has a maximum operation flow of 600 l/s, which means that the maximum flow that the source can supply to this network during the filling operation is limited by the limits of this pump, that is probably why, the maximum flow in pump l01 during filling phase is 570 l/s. Therefore, using the values of total inflow of node b02, which correspond to the flow in the pipe (p02) feeding the network (b01 is a dummy node), it is possible to observe that during the network filling, the total inflow in this node becomes approximately 2.6 times higher than in the continuous supply simulation. In contrast, in network 1, the flow in the supply pump (equal to the total inflow in node a02) becomes only 1.3 times higher than in the continuous supply simulation.

The high values of total inflow in the nodes observed after the start of the supply indicate that the flow of water in the pipes connected to these nodes is also high at the same moment. This is probably due to the higher pressure difference between the source and the rest of the network experienced during the filling phase.

The results suggest that the filling process of distribution networks tends to occur similarly in gravity-fed and pump-fed networks. However, the maximum pump flow rate can be one of the main limiting factors for filling time in pump-fed networks. In the case of gravity networks, this is driven by the piezometric head at the source. In addition, the filling pattern could be the result of a combination of different network characteristics, e.g. network size, topography and the connectivity between nodes, which varies from one network to another. Additionally, the air behaviour, entrapment and release, during pipe filling might play a relevant role. Nonetheless, there are some common points in the filling pattern of the assessed networks, such as: nodes closer to sources are more likely to be the first to be supplied, while those further away are more likely to be the last to be supplied; nodes with higher elevations are more likely to be supplied last, while nodes with lower elevations are more likely to be supplied first.

When the supply is turned off, the nodes in the networks are supplied by the volume of water existing in the pipes. Therefore, as depicted in Figures 5 and 6, in network 1, node a10 (the first node to become empty) is almost immediately empty after the supply is turned off (1 min), probably because the source is connected almost directly (via a pump) to the rest of the network. Whereas, in network 2, node b47 (the first node to become empty) takes 11 min to do so, this can be explained because of the fact that node DyNe_1 (dummy node) is at a higher elevation than the other nodes in the network, 40.52 m higher than the node in second place (node b01 is also a dummy node); in addition, the two pipes (link p01 and p02) connecting node DyNe_1 to the rest of the network have a volume of 15.55 and 46.45 m³.

The larger size of network 2 might be the reason for the big difference in the emptying time of this network (≃4:18 h) in comparison with network 1 (≃1:30 h). However, the nodal demand also contributes significantly to the emptying time of these networks. For comparison purposes, in network 1, nodal demand varies from 4.8 to 85.17 l/s; and in network 2, it varies from 0.1 to 10.3 l/s. Therefore, besides network 2 being larger, the consumption in the nodes is much lower than network 1, justifying the big difference in its emptying time. A pressure-driven demand approach with a minimum pressure threshold set to higher values than 0 m might become a relevant factor during network emptying.

In network 1, the first node to become empty is the node with the highest elevation in the network (node a10, 34.7 m), and the last node to become empty is the node with the lowest elevation (node a02, 10.2 m). This is clear evidence of the relevance that topography has in the emptying phase. In network 2, the first node to become empty in this network is not the node with the highest elevation. However, the first node to become empty (node b47) is among the nodes with the highest elevations in the network, being the third highest. Its position in the network and the shape of the network may have contributed to this, as the network has a group of main pipes connecting its different areas, and node b47 is situated in one of the most distant areas from the source. Similarly, the last node to become empty in this network is not the node with the lowest elevation. The node with the lowest elevation (node b57, 9.66 m) is the second last node to become empty; the last node to become empty is node b54, which has an elevation of 16.13 m, which is the fourth node with the lowest elevation. These results might demonstrate that besides the topography, the network topology is also an important factor in the emptying process.

From the graphs presented in Figure 7, it can be seen that the equity variation during the filling phase appears to have similar behaviour in different networks. During the phase in which the network is empty the D_E value is 0% (maximum equity), indicating that all nodes are equally unsupplied, this can also be termed as an undesired equity. The increase in the D_E when network supply begins is due to the fact that the network is leaving a situation in which the nodes are in the same condition (empty) to a situation in which some nodes begin to be supplied and others are not. The value of D_E continues to increase with the increase in the number of nodes to be supplied until it reaches a maximum value (minimum equity), which is expected when around half the nodes of the network are being supplied and the other half are not. After this moment, the increase in the number of nodes being supplied presumably means that the network is moving from a situation of maximum inequality in the network (maximum D_E value) to a situation in which all nodes are being fully supplied.

The behaviour of the D_E during the emptying phase is similar to that observed during the filling phase. Hence, before the supply is turned off, the D_E is equal to 0% because all nodes are being fully supplied. As soon as the supply is turned off, the value of D_E starts to increase because some nodes are no longer supplied. Similarly to the filling phase, the maximum D_E value is reached when approximately half of the nodes are filled and the other half are not. After the point of the maximum value of D_E, there are more empty nodes than those that are being supplied, so the value of D_E begins to decrease. At the final stage, the network is completely empty, making the D_E value 0%.

When the network is empty the VC equation does not produce values because the total available water in the network is 0, thus the equation results in a division by zero. It can be argued that it is not possible to speak of equity in the network if there is no water available. During the filling phase, the equity value increases, starting from the moment that the first nodes are supplied, meaning that more nodes are being supplied and/or the available water is being better distributed in the network. In the end, VC reaches the value 1 (maximum equity) when the network becomes completely full since 100% of the demand of all nodes is satisfied. In the emptying phase, the behaviour observed is the inverse of that observed in the filling phase, since the network starts completely full (VC = 1), and the value falls close to 0 until the last node is no longer supplied. In the end, when the network becomes empty VC equation does not produce values, as explained above.

VC brings a new and more complete perspective to the analysis of equity in the filling and emptying phases. As mentioned above, it analyses both the distribution of water among consumers and the level of satisfaction of the demand of the nodes present in the network, i.e. how much water one node is receiving in relation to the others on the network and whether the water needs of the nodes are being satisfied on that moment. On the one hand, D_E only provides a measure of the level of similarity of the water supply to the nodes in the network. According to Ameyaw et al. (2013), D_E measures the spatial uniformity of water supply within the network.

EPA-SWMM has demonstrated great potential for equity analysis in IWS systems, thanks to its capability to solve transitioning flows involving both pressurized and unpressurized (free-surface) pipe flows. Hence, when compared to standard modelling software EPA-SWMM provides a more accurate description of the network filling and emptying, which are frequent operations during IWS. In the present research, EPA-SWMM software enabled the analysis of the new equity index, i.e. VC, and its comparison with equity deviation index (D_E), for standard IWS operations.

Three factors affecting network filling and emptying have been studied, namely network size, topography, and water demand. Network size and the distance between the water source and supply nodes are dominant factors in any of the tested pipe configurations, with a direct effect on the pipe filling and emptying times. However, during the pipe filling phase topography seems to be as well a principal factor, clearly affecting pressurization times, especially in gravity-fed systems, while during the pipe emptying water demand seems to dominate. The results provided hereby show the impact of network size, topology, and demand on water supply equity.

On the one side, for fully filled and fully emptied network phases, the D_E value is equal to 0%, indicating homogenous conditions throughout the network nodes. During filling or emptying phases, the D_E value is greater than 0% reaching its maximum value when half the network is being supplied and the other half is empty. On the other side, the analysis of equity by means of VC exhibited a different pattern, in which VC does not have value when the network is empty, the minimum value of equity (VC tending to 0) was observed at the beginning or end of the network supply, and the maximum value (VC = 1) when the network was completely pressurized. The VC values during the filling and emptying processes varied between these two limits, increasing and decreasing, respectively.

The VC equation has shown a new perspective on evaluating equity in networks where both spatial distribution of water supply within the network and the satisfaction of the nodal demand are measured, considering the influence of nodal demand. The equation can also show the critically affected nodes in the network at every timestep. This can be used to study the reasons behind the disadvantage of some nodes and propose some interventions. The use of VC computation proved to be a highly beneficial method for understanding steady state during peak hours (critical hours) in the simulation, allowing evaluation of the state of each node at that simulation period.

With further research, EPA-SWMM can become a powerful tool for simulating, analysing, and studying specific moments in IWS that conventional modelling tools for water distribution systems are not able to simulate. It can thus be used by water utilities to minimize the impacts of IWS on the population by applying different methods (e.g. DMA), which can produce better results than the commonly used software, especially in some particular situations. Additionally, VC may allow the analysis, studies, and optimization of equity in situations of free-surface (unpressurized) flow, in a more reliable way than other equations found in the literature.

The following are some suggestions for further research:

• Equity analysis using VC computation could be extended to water supply systems affected by low pressures.

• VC should be considered as a well-suited index, in combination with EPA-SWMM hydraulic engine, for the implementation of optimization algorithms for the minimization of inequity in IWS systems.

• VC might be used to analyse the effect of private tanks in IWS networks.

The corresponding authors are thankful to the Ministry of Foreign Affairs of the Netherlands through SIDS and OKP Fellowships for sponsoring their MSc studies at the IHE Delft Institute for Water Education. The authors' theses are the basis for this paper. We acknowledge one of the authors of this paper N.T. who, unfortunately, is no longer with us (rest in peace), for his crucial contributions to the development of both theses that were the basis for this research.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.