Optimal consequence management of pollution intrusion into water distribution networks considering demand variation and pipeline leakage: a case study

Water distribution networks (WDNs) comprise each urban area's most critical infrastructure. These networks must deliver water to consumers to satisfy pressure and quality thresholds. Considering the high number of consumers of WDNs in urban areas, a disastrous situation may occur in case of pollution intrusion (Moghaddam et al. 2022). To minimize the adverse effects of contamination propagation in WDNs, a reliable strategy is an optimal consequence management (CM) plan considering the more realistic situation of WDNs during the crisis (Shafiee et al. 2018).

The first step in CM is to select the appropriate method for the hydraulic simulation of the WDN. Earlier studies tried to present CM by applying the demand-driven analysis (DDA) approach to their hydraulic simulation (Baranowski & LeBoeuf 2006, 2008; Poulin et al. 2008, 2010). This method results in inappropriate answers in abnormal situations. The DDA method assumes that the demand is not pressure-dependent and is constant; therefore, abnormal conditions may cause pressure deficiencies in some specific nodes (Tabesh et al. 2014). To overcome this issue, some studies applied pressure-driven analysis (PDA) (Alfonso et al. 2010; Zafari et al. 2017; Hatam et al. 2019). This method provides a more realistic view of a WDN's hydraulic condition when the system experiences abnormal conditions.

Most common CM strategies that applied simulation–optimization approaches minimized at least one of the following objectives (Bashi-Azghadi et al. 2017, 2018): (1) the number of operational interventions; (2) the consumed contamination mass; and (3) the number of polluted nodes. Preis & Ostfeld (2007) implemented a multi-objective optimization model to minimize the pollutant consumed by users and operational interventions using NSGA-II. Alfonso et al. (2010) implemented GA (for single-objective optimization) and NSGA-II (for multi-objective optimization) to minimize the number of polluted nodes and operational interventions. Unlike other pieces of research that focused on other objective functions (OFs) like maximizing flushing flow, minimizing distance traveled for operational intervention, unsuccessful flushing, water age, and water quality sensors numbers (Shafiee & Berglund 2015; Zafari et al. 2017; Bazargan-Lari 2018; Ciaponi et al. 2019), in current research, the focus is on two OFs. First, minimizing the total consumed contaminated water, and second, minimizing the operational interventions (valve closure/opening). This helps us minimize the pollutant's adverse effect on public health and operational costs.

In addition to hydraulically controlling pollution propagation, authorities can issue water advisories to limit the consumption of contaminated water by encouraging users to suspend their usage temporarily (Shafiee et al. 2018). Most studies neglected the immense effect of water demand variation during pollution intrusion incidents in their CM plan. Water demand changes can significantly change the network's hydraulic status and, consequently, the CM output. Preis & Ostfeld (2007) considered demand changes in their CM model by assuming that 30% of consumers continue their usual water consumption behavior and the remaining stop water usage. Several studies introduced agent-based models to simulate contaminant events in WDN and manage threats considering consumers' reactions to such events (Zechman 2011; Shafiee & Zechman 2013; Shafiee et al. 2018; Kadinski et al. 2022). Shafiee & Zechman (2013) introduced a socio-technical agent-based model in which consumers can reduce their consumption to address socio-technical aspects of pollutant intrusion in WDN. Then the reduced demand was applied in the hydraulic simulation.

Despite numerous studies discussing a wide range of CM plans and strategies, there is still a need to bridge a gap between simulation results and the actual situation of WDN during the contamination period. Most papers focused on optimization methods (algorithm) and/or OFs, while other factors related to WDN are yet to be examined. Factors like water demand variations during pollution incidents and pipeline leakage are necessary to be considered to achieve more reliable and realistic outcomes and mitigate the pollutant's adverse effects on people. To the authors' knowledge, the pipelines' leakage effect in the CM plan is not addressed in previous studies. Therefore, this paper aims to address a more realistic optimal CM strategy by developing a hydraulic simulation model that considers the actual water consumption scheme during the contamination intrusion as well as the WDN leakage.

To do so, water end users were asked to fill out the questionnaire to measure water demand changes during pollution incidents. Also, the minimum night flow (MNF) method was utilized to measure WDN's leakage. Moreover, PDA was implemented to perform hydraulic and water quality simulations. In addition, the multi-objective optimization method (NSGA-Ⅱ) was utilized to obtain the Pareto front of optimal solutions regarding OFs.

Considering all these issues, scenario-based simulations will better represent the WDN situation while facing contamination events and create a better opportunity for decision-makers to manage the pollution incident better.

This paper explicitly tries to answer the following questions:

• 1.

  At what levels will water demand variations affect CM outcomes?

• 2.

  How will considering WDN's leakage affect CM outcomes?

The rest of the paper proceeds as follows: Section 2 illustrates the problem description, simulation model, and methods used in this study. The case study is explained in Section 3. The results of the analysis are introduced in Section 4. Then, the discussions are drawn in Section 5. Finally, the conclusion is presented in Section 6.

Water demand and its changes are among the main factors affecting the hydraulic performance of a WDN (e.g., nodal pressure and water velocity). Therefore, any change in nodal water demand will affect the optimal response to contaminant intrusion. Any warning about the contaminant intrusion into the WDN will affect the water consumption behavior (Zechman 2011; Strickling et al. 2020). In the case of pollution entry into WDN, the authorities may warn people whether by ‘Do not use’ or ‘Boil water’ notice due to its potential health risks. These procedures are described by EPA (USEPA 2013). The current paper addresses water demand changes by evaluating consumers' reactions to such incidents through questionnaires, as Lindell et al. (2010) did.

To investigate demand changes, the authors specifically developed an appropriate questionnaire for the current study asking about water usage that consumers will continue during the contamination period. However, some people probably need to be aware of pollutant intrusion and continue their water usage as usual. Therefore, it is considered that a percentage of people continue their usual consumption.

A total of 120 respondents were selected randomly and interviewed in person. All respondents were connected to WDN. The interviews were conducted with one of the household members on behalf of the others living in the home. All water activities are categorized into three groups: drinking, sanitary, and unhygienic. Cooking and drinking are included in drinking usages; water used for shower, washbasin, cloth, dishes, and cleansing represent sanitary usages, and flush tank and green area irrigation represent unhygienic usages. Socio-economic variables considered while filling out the questionnaires are gender, level of education, age, employment status, marital status, having a child under 5 years old, the experience of similar events, and household expenses (Siegrist & Gutscher 2008; Marks et al. 2016). Survey data revealed that about 60% of respondents were under 30, 51% were female, 68% were single, 18% of married ones had children under 5 years old, and 50% were employed. Two-thirds of them had a higher education degree.

is the leakage rate of the network when MNF occurs, represents the minimum flow during the night, and is normal domestic night-time usage. The term NDNU is used here instead of NU (Night Usage) because it was assumed that there are only household users in the study area. If there is no real measurement for determining the MNF, it can be determined using the daily water demand pattern (AL-Washali et al. 2018), as the current study considers. NDNU is calculated by multiplying the active population at night by their normal night-time water usage.

Minimization of the adverse effect of the pollutant on public health and operational interventions were considered two OFs of this study. Also, the Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ) was selected as an optimization algorithm. NSGA-Ⅱ was chosen for the optimization method, which has already been used in many similar types of research (Preis et al. 2007; Alfonso et al. 2010; Rasekh & Brumbelow 2014; Bashi-Azghadi et al. 2017, 2018; Bazargan-Lari 2018; Ciaponi et al. 2019). The algorithm works through these six steps (Deb et al. 2000):

• 1.

  Initial population generation by setting random strings (chromosomes);

• 2.

  Evaluation of each string's fitness for all objectives;

• 3.

  Sorting strings into Pareto fronts which each chromosome will be ranked through a non-domination algorithm;

• 4.

  Crowding distance sorting within each Pareto front. Each front will be sorted using the crowding distance of each member. The crowding distance of each chromosome is the average distance between the fitness vector of all objectives of the chromosome and the fitness vector of all objectives of other members of that front.

• 5.

  Generation of a new population using GA operations (selection, crossover, and mutation); and

• 6.

  Stopping condition.

The most common criteria used for the termination of the algorithm consist of generation number limit, fitness value limit, and run-time limit (Bashi-Azghadi et al. 2017, 2018). In the current study, both the generation number limit and fitness value limit are considered as the algorithm termination criteria. The algorithm will be terminated if either one of these two criteria are met.

In the current study, the harmful pollutant concentration threshold is considered 0.05 mg/l, and the rate of pollutant entry is assumed to be 1,000 g/min (Zafari et al. 2017). The initiation time of pollution entrance to the WDN is set as 11:00 AM, which continues for 4 h (from 11:00 AM to 15:00). The water demand rates during this time interval present the worst case that could happen in the aspect of pollution propagation. The first node after the reservoir was selected for pollution entry because they are the most critical node for pollution injection (Zafari et al. 2017; Razavi et al. 2023).

CM starts 4 h after contamination entry (Zafari et al. 2017). This gap is because of the time needed for detection and reaction to pollution intrusion into the WDN, based on historical data about the study area. Therefore, 4 h is considered as the water utility's response time. Three hours after the pollution intrusion (from 14:00), when the pollution is detected in the WDN, officials start to inform people about the event (warning time).

At the beginning of the simulation, all FCVs are open, and the hydrants are closed. By the start of CM activities at 15:00, the status of valves will change and remain constant until the end of the simulation period, which lasts 24 h. Water quality analysis will also be performed to calculate the concentration of a pollutant at nodes with 3-min time steps when the contaminant enters the network. Desired pressure head is assumed to be 30 mH₂O, and the minimum pressure head is zero. Defining minimum pressure to zero may bring operational problems that are part of this study's limitations.

Four different scenarios were considered in this study to investigate better the effect of demand variation and pipelines' leakage on the CM plan.

The shares of water activities that will continue during the study area's contamination period were examined. As shown in Table 1, less than 0.5% of people continue drinking and cooking with contaminated water. After analyzing data obtained from 120 respondents, the consumption reduction rate while pollution is confirmed in WDN is 88%. This study assumes that 20% of people will continue their normal water usage without any change because they are unaware of water pollution in WDN or may not take warnings seriously, as Preis & Ostfeld (2007) and Lindell (2018) considered. Therefore, there will be a reduction of about 68% in demand in the study area. Therefore, the water demand considered in the model is 80 lpcd.

Access limitations to acquiring actual data make authors calculate leakage through data provided by simulation results. The MNF method was used to address the network's leakage rate. According to the daily demand pattern, MNF occurs at 4 AM, with a rate of 55.23 l/s, while the average pressure of the network at this time is 46.8 mH₂O.

As CM results are divided into four different scenarios, the main characteristics of these scenarios are summarized in Table 2.

Maximum NPN is calculated for this scenario, equal to 33,497. Hence, 33,497 nodes experienced a pollution concentration of more than 0.05 during the simulation period at each time step. Selected valves and TCE regarding optimization results are presented in Table 4. According to the results, V1, V3, V6, and H4 were the most chosen valves in most results sets. The given results in Table 4 which refer to the base scenario, the mostly selected valves are located close to the reservoir where the pollution intrusion happens. Therefore, closing these valves prevents further pollution of the network. Furthermore, the selected hydrants are located at a point that could be the destination of waterflow in WDN. In that case, it can efficiently take out the pollution from the system.

Table 5 shows a different set of valves the optimization model selects when various operations are considered. Besides a considerable reduction in TCE, there is a difference in the chosen valves compared to the first scenario. Regarding the differences in results of different scenarios, it should be mentioned that, in each scenario, the hydraulic condition of the WDN, including pipes flow and its direction as well as velocity change due to changes in water demand. As a result, the pollution propagation scheme in WDN changes considerably, so that different valves and hydrants are used for control of pollution propagation and taking it out of the WDN. This disparity is evident in Table 5, wherein the most selected valves in Sc. 2 are H2, V1, V2, and V3, diverging from those in Sc. 1.

NPN in the last scenario of this study is 34,932, which indicates a considerable surge compared to Sc. 1. Table 7 shows the five different sets of actions and the amount of contamination exposure. Whether comparing the TCE or set of actions proposed by the optimizer, there is a meaningful difference in the CM output between this scenario and the other ones.

Different scenarios show a significant change in the TCE compared to Sc. 1, where demand and/or leakage are not considered without executive action. This indicates that neglecting demand changes and leakage leads to incorrect estimations of the network's hydraulic and water quality status. Furthermore, the selected valves may not be optimal for controlling and removing pollutants. Each scenario imposes its unique hydraulic situation on the CM output. This is the main reason that each scenario has a different CM output. Demand reduction leads to maximum contaminated nodes (maximum NPN). At the same time, the scenario with leakage consideration makes contaminated nodes the minimum ones. Using Sc. 4 makes it possible to reduce about 32% of polluted water exposure without employing any administrative operations, whereas employing all capacity of valves in Sc. 1 merely reduces contamination exposure by nearly 26%. These reports acknowledge the fact that demand and leakage are highly effective when it comes to deciding the proper action in CM plans during the contamination period.

Any changes in water demand will play a significant role in changing the hydraulic state of the water network and the contamination propagation, consequently, the outputs of CM. When demand reduction applies, a 30 kg reduction occurs in contamination exposure. Leakage modeling (Sc. 3) lessens the TCE by about 13 kg. In other words, 13 kg of polluted water is getting out of the system through leakage, which Sc. 1 does not consider in the results. By utilizing a set of operational actions in this scenario, there would be a 10 kg reduction. Scenarios 2–4 encompass the analysis of demand variations occurring during pollution intrusion periods, network leakage, and the simultaneous simulation of these events. The inclusion of these factors significantly impacts the hydraulic and quality conditions of the network. Consequently, nodal pressure, velocity, water age, pollution propagation, flow rate, and flow direction exhibit differences compared to Sc. 1, which does not account for such factors. Therefore, the varying selection of valves by the optimizer in different scenarios can be attributed to these influential factors.

The leakage amount in this research was estimated to be 20% of the total water demand, which might appear substantial. However, it is essential to note that this value is derived from existing literature and previous studies conducted in similar regions to the study area. For example, Serafeim et al. (2022) highlighted that outdated and poorly maintained WDNs could lead to actual losses reaching as high as 70–80% of the system input volume. Conversely, well-maintained and monitored networks might experience only a 7% loss of the system input volume. Additionally, AL-Washali et al. (2018) reported a leakage rate of 24.1%. Furthermore, research by Ghobadian & Mohammadi (2023) and Negharchi & Shafaghat (2020) indicated leakage percentages of 12.7–29.4% and 28–37%, respectively, in a case study conducted in Iran, which is where our study area is also located.

NPN in Sc. 2 is 35,816, which means 35,816 nodes were infected during the simulation period. Although contamination exposure noticeably declined, NPN surged due to the more extended presence of contamination in the network. Before 3 PM, when the water demand pattern is under normal conditions, the pipes' flow and velocity are higher; therefore, the pollution propagation speed is higher. A more significant part of the network is expected to be contaminated. However, after demand reduction, the pipes' velocity reduction leads to a more extended existence of contamination in the WDN. Therefore, it is inferred that if no action is taken, demand reduction causes an increment in the number of contaminated nodes (compared to Sc. 1). There is a gentle reduction in the maximum NPN from 33,497 in Sc. 1 to 32,996 in the third scenario. Therefore, leakage consideration reduces the pollution propagation in the WDN.

Table 8 summarizes the results of different scenarios considered in the current study. The minimum and maximum pollution exposure, maximum infected nodes, and some operational interventions are presented in this table.

According to Table 8, the lowest NPN occurs in Sc. 1, while the highest happens in Sc. 2. Although leakage and demand reduction in Scenarios 2 and 3 caused a decrease in TCE by consumers, the most reduction occurred in Scenario 4 (32%). Minor exposure occurred in Sc. 4 by 124.44 kg. These measurements demonstrate the considerable role of these considerations on the CM output.

In this study, the optimal CM of pollutant entry into the WDN was done under two OFs minimizing the TCE and minimizing executive operations. According to existing related works, these OFs are a good indicator of public health status and administrative costs. NSGA-Ⅱ algorithm was utilized for this purpose.

This research tried to make the WDN simulation closer to reality during the pollution intrusion to achieve more reliable results for CM. For this purpose, the effect of demand change during the pollution incident and pipelines' leakage on the CM results is investigated through four scenarios. According to the results, the total daily leakage of the network is about 20% of the total nodal demand, and 88% of the water demand will be reduced when such an incident happens. The first scenario's results were reported without demand variation or leakage effects. The second scenario measured the impact of water demand variations on CM outputs. The third scenario reported the effects of the pipeline's leakage on CM outputs. Eventually, the fourth scenario reported the effects of simultaneous consideration of demand changes and leakage. It can be argued that the scenario of considering both leakage and demand changes should be used as a basis for decision-making about the CM since this scenario's proposed decisions are closer to the network's actual state than the others.

The model introduced here does not consider uncertainties about contamination source identification, pollution concentration, time, and duration of intrusion, but it is developed for the worst-case scenario. In the current study, the pollution intrusion node, time and period of intrusion, and its origin are assumed to be predefined. Therefore, further studies must undertake these uncertainties to address a more realistic situation. In addition, the hydraulic and leakage models need to be calibrated due to a lack of appropriate data. The nodes in which demand reduction occurs in this study, due to the almost small size of the network and lack of sufficient data, are assumed to be all consumption nodes, which is not a realistic assumption. Hence, there should be further studies to bridge this gap.

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

The authors declare there is no conflict.