Resilience analysis of water supply systems
Contemporary society is dependent on water and the supply of water is threatened by a number of factors, including population growth and associated urbanisation along with climate change. On a global scale these problems mean than increasing proportion of the global population will be in water stress in the next decade, a situation that will be exacerbated by climate change and global warming. On a national scale community in the United Kingdom could experience droughts, increased extreme weather events and flooding over the coming decades, all of which will adversely affect the supply of water. There is a strong case for improving the resilience of water supply. This research explores resilience of water supply systems.
Resilience analysis requires a detailed understanding of supply network functions, the need for design optimisation balancing supply and cost and the flow characteristics of a water supply and distribution network in a region. Resilience must be considered in terms of design resilience which determines how a system will behave in unforeseen events and operational resilience which determines the way in which a system will behave when affected by predicted risk-events.
This process can be difficult as it first requires knowledge of possible threats to supply and detailed knowledge of the actual performance of the system. One solution is to focus on the water network as a system, testing resilience of that system to changes in operational flow and demand. This can be achieved using modelling software such EPANET.
Summary of the Literature Review
The water supply network is critical infrastructure which needs to be reliable and robust. However, this requires an understanding of the manner in which the supply network functions, the requirements of optimal design balancing energy consumption, supply and costs with sufficient resilience to events that could interrupt this vital commodity. There is a need to ensure that the water supply and distribution network has sufficient attribute -based resilience to unforeseen events, with inbuilt limits on the duration and magnitude of adverse impacts on the supply. It must also have performance-based resilience whereby the system can withstand known threats, with minimal disruption to operational performance. The difficulty is in determining these hazards and quantifying the risks associated with these hazards and then applying this data to what can be an extensive and complex network. The solution is to focus on the water network as a system and considering the possible modes of failure of that system rather than trying predict all possible threats. There are a range of methods of analysis including software such as EPANET which is useful in determining the operational capacity of a network.
It is a fact of life that human existence is dependent on water either as a source of hydration or a means of growing sufficient food stocks to maintain health and nutrition. Water is also a valuable element in health protection and the prevention of diseases and contagions. The supply of clean water and the removal of foul water underpins every aspect of society facilitating industry and commerce the tourist sector, agriculture and urban development (Pond and Pedley 2016, chpt 12) Water has become a precious commodity, with many national government’s privatising the water system, including the provision of potable water and sewage systems to offload the public cost of supply and the burden associated with the risk of supply interruption (Bakker 2010, pp.2-8). However, it is suggested that over the past century with the evolution of water treatment facilities and the fact that the majority of properties, at least in the developed world, have clean, running water within their properties, means that contemporary society takes water supply for granted (Pond and Pedley 2016, chpt 12). This research considers water supply systems and the need for resilience in these systems. It explores methods of risk analysis in water supply systems. This chapter sets the research in context, providing a background to the problems of water demand and supply, setting the case for the need for resilience analysis. This chapter also presents the aim and objectives of this study.
Factors Contributing to Water Stress in Contemporary Society
However, water is a finite natural resource and cannot be created, which means that supply is dependent on the hydrologic cycle that recycles water through the atmosphere (Population Institute 2010, p.1). It is argued that this cycle faces two major challenges threatening water supply and resources namely population growth and climate change. Current statistics estimate that the global population will increase to 9 billion people by 2050, an increase of 3 billion since 2010. It is further estimated that 90% of these additional people will be living in developing countries, the majority of which are already in water stress (Population Institute 2010, p.2). For the purposes of clarification, it is noted that water stress is a means of measuring the imbalance between the demand for water and available sources of water, with the European Environment Agency (2017, p.1) pointing out that water stress occurs when demand for water exceeds the available amount during a certain period. This can be the result of climate induced drought or poor quality water reserves which restricts its use. It is caused by deterioration of the quantity of available fresh water resources through the over-exploitation of aquifers or dry rivers and/or issues with the quality of available water through eutrophication or organic matter pollution.
- Global Population Growth
Global population growth, which affects water consumption in two ways, the first is through increased water consumption and the second is the spread of urbanisation which follows population growth. In consumption terms, the Population Institute (2010, p.1) estimates that global water consumption rate effectively doubles every twenty years. This means that if population trends persist then demand for water, drive by population increases only will surpass water availability by 56%, with the result that by 2025, an estimated 1.8 billion people across the globe will live in regions of water scarcity (Population Institute 2010, p.1).
Population growth leads to the spread of urban development, with the global population transitioning from a largely agrarian society at the start of the 19th century to an urbanised society. To put this transition in context, it is noted that more people now live in urban areas than in rural areas, equating to 54% of the world’s population living in urban areas in 2014 compared to 30% in 1950. This figure is predicted to increase to 66% by 2050, with the most urbanised regions including Northern America where 82% of the population living in urban areas and 73% of the population in Europe living in urban areas. While these regions will continue to urbanise, the biggest increase will be in developing nations such as Africa and Asia where 40 and 48 per cent of their respective populations currently live in urban areas, with predictions that this will increase to 56 and 64% respectively, by 2050 (United Nations 2014, p.1). This is likely to put even greater pressure on dwindling water stocks due to large concentrations of people in water scarce areas (Population Institute 2010, p.2).
- Climate Change
At the same time, contemporary society is threatened with climate change, created by an imbalance of greenhouse gases in the earth’s atmosphere and which is slowly leading to warming of the earth’s surface. This phenomenon is predicted to increase the frequency of extreme weather events, with some regions affected by increased and more extreme flooding, while others could experience prolonged drought (Hardy 2003, pp.3-8). While it is difficult to pinpoint the exact locations of these impacts, the Intergovernmental Panel on Climate Change (IPCC 2015, pp. 79-113) suggest that coastal areas will be affected by rising sea levels due to melting polar ice caps and inland areas could be affected by increased fluvial flooding in extreme rain events. The fact is that every region will ultimately be affected due to population migration from the most affected areas with global disruption of food supplies and shrinking water reserves. These events will also increase the risk of water contamination putting further pressure on water supply services.
To put these risks in context, the IPCC (2015, p. 79) make the point that based on current forecast data that by 2025, water availability in nine countries in the east and southern regions of Africa will be less than 1,000 m3 /person/yr, with another twelve countries having 1,000–1,700 m3 /person/yr water. This means that an estimated 460 million people will be at risk of water stress, the majority of whom will be in western Africa. It is noted that these estimates are based simply on population growth and do not take account of the potential impacts of climate change, which could conceivably increase these risks, with current estimates suggesting that the African population at risk of water stress and scarcity could increase from 47% in 2000 to 65% in 2025 (IPCC 2015, p.79). It is suggested that this discourse highlights the challenges faced by global society in relation to water and the fact that this is a critical infrastructure. Globalisation, urbanisation and climate change also put pressure on urban drainage systems with increased threat of the additional flow volumes, the need to prevent pollution of potable water resources and the ability to recycle this water to relieve pressure on potable water for non-drinking purposed (Mugume et al. 2015, p.27).
It would be easy to assume that these problems are confined to Africa and Asia, however Butler et al. (2014, p. 347) point out that climate change projects for the United Kingdom (UK) suggest significant rises of average summer temperatures by 3-4°C, with wetter winters and more frequent, extreme weather events by 2080. The impacts of climate change are already being experienced with for example England and Wales experiencing “one of the ten most significant droughts of one to two year’s duration in the last 100 years up to March 2012”, with hose-pipe bans in the south-east of England (Butler et al. 2014, p. 347). The UK experienced significant changes in weather patterns towards the end of 2012, which resulted in the second wettest year on record. These events adversely affected the water supply and promoted calls for a greater sustainability and resilience of critical infrastructure.
There are a range of possible impacts of these increasing risks of water stress which apart from the threat to human health and life, could also lead to conflict over water rights and supplies (IPCC 2015, p.79). Mugume et al., (2015, p.27) add that there is also an urgent need to build greater resilience into urban drainage systems.
In short there is a dire need to build resilience into the water cycle with Ahern (2011, p.341) arguing that this is essential to create a sustainable water supply. In the immediate term, it is noted that a water supply system can fail in many different ways resulting in loss of water, economy, and even people’s life. Hence, water systems should be resilient and it is suggested that evaluation of the current resilience level of water supply systems is crucial.
- Aim and Objectives
The aim of this study is to explore resilience analysis of water supply systems. The objectives of the research are to
Illustrate the basic concept and methods for resilience analysis of water supply systems
Carry out resilience analysis for several simple and small scale water distribution systems using software such as EPANET
Identify the features of those systems’ resilience and/or the potential problems lie in the systems.
- Literature review
A critical review of pertinent literature was carried out as part of this research, referencing academic journals, water industry publications and books, along with reliable Internet sites such as those hosted by the United Nations and software suppliers. The purpose of the review was to explore the objectives further, to understand the concept of resilience in detail and the types of resilience models that are available in water engineering.
Resilience Johansson et al. (2013, p.27) makes the point that society depends on these services, including water and it is therefore crucial that this critical infrastructure is reliable and robust. This in turn needs a robust understanding of the inherent vulnerabilities of water resources and the risks posed to supply. Johansson et al. (2013, p.27) implies that this requires sufficient knowledge about the water system to build greater resilience, using reliability analysis and vulnerability analysis. Reliability analysis focuses on the ability of the system perform its intended function, whereas vulnerability is a measure of the system’s inability to withstand strains and the impacts of the consequent failures.
Resilience is defined as “the degree to which the system minimises level of service failure magnitude and duration over its design life when subject to exceptional conditions” (Diao et al. 2016, p.383). Mugume et al. (2015, p.16) suggest that resilience can be classified into two categories namely general resilience and specified resilience. General resilience, also referred to as attribute -based resilience is described as the state of the system that enables it to limit failure duration and magnitude to any threat including known and unknown threats. Specified resilience also termed performance-based resilience is linked to known threats, and refers “the agreed performance of the system in limiting failure magnitude and duration to a given (known) threat” (Mugume et al. 2015, p.16). In other words, attribute-based resilience assesses the system as a whole, considering system design issues, to foster an appropriate response to threats to the water supply cycle whereas performance-based resilience is more prescriptive, referring to the agreed performance of the system in response to a specific threat (Diao et al. 2016, p.383).
Butler et al. (2014, p. 351) also discusses resilience in this manner, suggesting that attribute-based resilience, concerns the system as a whole, is descriptive in nature and can be considered as a set of design principles. As such attribute-based resilience could also be referred to as design resilience. Performance-based deals with performance of the system and the need to limit the duration and magnitude of failure for each given threat. Thus, this process is typically quantitative and refers to operational rather than design goals and can therefore be referred to as operational resilience. Butler et al. (2014, p.351) add a third form of resilience, namely technology-based resilience which refers to equipment that can be developed and implemented to improve the preparedness of the end-user such as water companies and suppliers for extreme events.
Determination of Resilience in Water System It is argued that in order to determine the resilience of future water supplies it is first essential to understand the inherent resilience of the underlying system. However, this process is influenced by a range of factors, including the need to link threat to the impact of that threat and developing ways of managing different types of threat that have the same impact and similar threats which have different impacts. Other challenges include developing ways in which all possible potential threats can be identified and then evaluated, whilst building sufficient contingency into a system to take account of unforeseeable threats (Diao et al. 2016, pp.383-384).
Many of these issues can be managed through the use of risk analysis, which is useful in identifying threat-impact relationships. This is typically achieved in a staged process, starting with the identification of all potential hazards which affect a system or a process. This can be carried out by brainstorming, using logic trees or by drawing on experience of previous events. Once the potential hazards are identified each can then be considered in terms of the likelihood of occurrence and the impact of such an occurrence using quantitative or qualitative reasoning and analysis. The risk assessment process will highlight the key risks to a system or a process and the design team or analyst can then develop suitable mitigation measures to avoid, off-load, resolve or accept these risks. (Arnaud et al. 2013, pp.50-52; Meyer and Reniers 2016, pp.39-42). However, Diao et al. (2016, p.384) make an important point, agreeing that risk management is an essential factor in resilience engineering but adding that this process does not address yet unknown threats. Another consideration is determining which failure modes to explore, or which are likely to occur. Ideally this process should encompass examination of the multiple failure scenarios associated with each failure mode. For example if the failure mode is pipe failure then the failure scenarios may include every potential combination of pipe failures in the network, with stress scenarios ranging from 0% to 100%. In this assessment, different stress scenarios can be assessed with likelihood of occurrence from high probability routine failures such as a single pipe failure to low probability failures such as the entire network shut-down as occurred following the earthquake and tsunami in Japan in 2011 (Johansson et al., 2013, p.29; Diao et al. 2016, p.384).
The last example highlights the challenge for effective system design, as it is unlikely that designers in Japan could have predicted the earthquake, the consequential tsunami and the impacts of these events which occurred in close proximity (Diao et al. 2016, p.384). Gheisi and Naser (2014, p. E319) argue that it is difficult to assess vulnerabilities in water distribution systems (WDSs) simply because of the numerous challenges faced by providers in supplying water. These systems can be subjected to multiple failures in the WDS at the same time particularly in older networks or in systems subjected to variable and harsh climatic conditions.
A solution to this problem is to focus on the system and the possible modes of failure of that system rather than trying to understand and predict all possible threats. For example, it is feasible to explore the impact of the risk of pipe failure in a water distribution systems, by considering the potential hazards to that system which could include internal failure modes such as corrosion or external failure modes such as subsidence. The point being that these are realistic threats that can be addressed to increase the resilience of supply (Diao et al. 2016, p.384). Gheisi and Naser (2014, p. E319) argue that this process is influenced by the input information in the analysis on the basis that a higher level of reliability can be achieved if the analysis is based on the realistic assumption of simultaneous failure.
There are different levels of system analysis including global resilience analysis (GRA), Mugume et al. (2015) suggest is an effective method for assessing whole-system resilience of engineering systems. Vasan and Simonovic (2010, p.279) suggest that it is also important to understand the resilience of a water distribution network which includes an understanding of the design of these systems including design optimisation and demand within the network. It is suggested therefore that to facilitate discussion of resilience analysis of water systems it is prudent to understand the underlying factors which affect design of the water distribution system.
Water distribution network design
According to Cubillo and Pérez (2014. p.355) the water supply and distribution service provided by any given water distribution network is typically measured by interruptions to the service in a specific time interval. It can also be measured by the degree of non-compliance with designed or the required operational standards in place for the service. It is acknowledged that all systems are subject to a degree of risk in relation to these required operational standards however the aim of resilience engineering is to minimise these risks whilst optimising the design of the network. De Corte and Sörensen (2014. p.333) point out that water distribution network design (WDND) involves a range of data and problems including the optimisation problem, whereby designers must choose the optimal diameter for each pipe within the network layout, ensuring that supply satisfies demand and that this is carried out in a cost-effective manner and ideally using a gravity-fed system.
Cubillo and Pérez (2014. p.356) maintain that the approach to network design and assessment should consider the different risks associated with that system including risks to the structural elements of the network and the likelihood of breakage or structural dysfunction of different elements within that system. This must take account of the inherent characteristics of the system including pipe diameter and material, the service life and operational age of the system. This data can be used to determine the probability of an event occurring which could subsequently interrupt supply, through statistical analysis of past performance. The WDND is also designed to take account of the risk at consumption points, such as the possibility of supply interruption at an individual property or group of properties. This could be due to problems with pressure and/or the quality of water. Therefore, the risk assessment should take account of the topography of the region being supplied along with the location and the network configuration. Other factors which will influence the risk assessment include operational capacity of strategic water network elements such as treatment stations and abstraction points, pumping stations and sector inlet pipes. These processes can be used in determining the overall system risk, which Cubillo and Pérez (2014. p.356) suggests equates to the sum of the risks of all individual elements in the distribution network, including service connections. It is argued that the outcome of this process means that the status of the network can be determined, thus providing a useful starting point for resilience analysis of the network.
Prasad and Park (2004, p.73) adds that effective resilience is a product of the design process which seeks to minimise network costs and optimise reliability. In physical terms this can equate to the provision of excess head above the minimum allowable head at each node in the distribution network whilst designing reliable loops with practicable pipe diameters.
This process may appear straightforward, as Creaco et al. (2014, p. 379) point out that a direct estimation of service reliability can be measured using a range of specific performance indicators including for example the ratio of water discharge supplied to the corresponding water demand under differing operational scenarios. However, the process can be complex because of the wide range of operational conditions and critical scenarios which can affect a single network with implications for the wider system. As a result, reliability, can be expressed through what Creaco et al. (2014, p. 380) term indirect indices such as resilience and modified resilience using a single hydraulic simulation, to determine the redundancy of the network within a given set of benchmark operation conditions.
Ramana et al. (2015, p..496) adds that assessing flows within a water pipe network can be complex as it requires the computation of flows and water pressures and a complex layout and varying pipe diameters. If the system is based on gravity feed, then the behaviour of a network could be assessed as a sequence of steady state conditions. However, the accuracy and reliability of this process requires analysis for changing patterns of consumption and/or delivery. It also requires analysis of the impact of elements within the water distribution network such as booster pumps and pressure regulating valves which can change the flow within the system.
There are several different methods that can be used to compute flows in a water distribution network ranging from graphical methods, the use of physical analogies and mathematical models. One mathematical method of analysis is the Hardy Cross Technique, which Ramana et al. (2015, p.496) suggest seeks to account for the uncertainties inherent in demands, as well as variability in pressure heads and pipe roughness coefficients. Essentially it was tried to resolve the optimisation problem using a non-linear programming model and a generalised reduced gradient method. Other models compute the reliability of water distribution system by treating these variables as random or assuming that water demand and pipe roughness coefficient can be assess using probability distribution and hydraulic simulation of pressure heads at the demand nodes. Ramana et al. (2015, p.496) add that there is software available to facilitate analysis of nodal and system hydraulic reliabilities, including for example EPANET.
The EPANET software was developed by the Environmental Protection Agency in the United States of America (USA) and has the capacity to analyse unlimited number of pipes and tanks. EPANET is essentially a computer programme that can be used to perform simulations of hydraulic and water quality behaviour for specific periods of time, within pressurised pipe networks Thus it is useful in analysing both simple and complex water distribution networks. The programme assumes a network consists of pipes, nodes (pipe junctions) and pumps, along with valves and storage tanks or reservoirs. The model tracks the flow of water in each pipe, whilst calculating the pressure at each node, and the concentration of a chemical species throughout the network. The aim of the programme is to improve the understanding of the movement of potable water constituents within a water distribution system (Ramana et al. 2015, p.497; Rossman 2000, p.9; Sayyed et al. 2014, p.626). Rossman (2000, p.9) adds that EPANET can also be used for different kinds of applications in distribution systems analysis including sampling programme design and hydraulic model calibration. Other uses include analysis of residual chlorine and consumer exposure assessment to chemical content in the water supply. It is a useful tool in assessing alternative management strategies for improving water quality by testing alternative sources within multiple source systems and altering pumping schedules. It can be useful in assessing the resilience of a network, by analysing pipe replacement. EPANET can be used to determine and assess hydraulic performance under different flow conditions as it does not place a limit on the size of the network and uses established mathematical concepts and theories such as the Hazen-Williams, DarcyWeisbach, or Chezy-Manning formulas to determine friction losses in the network. It can also be used to model constant or variable speed pumps, computing pumping energy and cost (Rossman 2000, p.9; Georgescu et al. 2015a, p.1013; Muranho et al. 2014, p.1201). Georgescu et al. (2015b, p. 660) provides a good example of the use of EPANET in a case study points on the water distribution system of Buzau City, described as a medium-sized city in South-Eastern Romania. The research involved the construction of a simplified numerical model of city’s main water distribution system using EPANET. The model was used to connects the city’s four pumping stations to 45 booster stations and other users. The model was then calibrated using real-time data recorded from 2014, as shown in Figure 1.
Figure 1 Water Network Buzau City modelled for EPANET (Georgescu et al. (2015b, p. 664, Figure 3, table 2)The model was useful in establishing the pumping scheduling in terms of pressure, taking account of the discharge pressure at the pumping stations and the requested or demand pressure at key points in the network. The model was also useful in calculating energy consumptions which could then be compared with available data. The data was useful in assessing and rationalising energy consumption in the distribution network. It is suggested that it could also have useful in rationalising the performance of the network and testing the resilience of the system.
The methodology of this study is to explore resilience analysis of water supply systems. The objectives of the are to
- Illustrate the basic concept and methods for resilience analysis of water supply systems
- Carry out resilience analysis for several simple and small scale water distribution systems using software such as EPANET
- Identify the features of those systems’ resilience and/or the potential problems lie in the systems.
A system’s resilience is been tested using basic failure modes with increasing stress magnitude and estimating the corresponding strains that arise (Johansson, 2007;Hokstad et al., 2013). The Technique includes the following test:
Step 1. Determine and identify the failure mode that has been given (e.g. structural failure, excess demand); the failure mode that has been chosen is fire mode.
Step 2. Once opening each network using EPANET, to run the simulation on which the peak time of water demand is determined.
Step3. Find the necessary system stress / strain and the way simulate it.
Step 4. The following equations can be used to determine the total number of random times along with the minimum and maximum rand percent inherit last rand.
Creaco, E., Fortunato, A., Franchini, M. and Mazzola, M.R., 2014. Comparison between entropy and resilience as indirect measures of reliability in the framework of water distribution network design. Procedia Engineering, 70, pp. 379 – 388.
Cubillo, F. and Pérez, P ., 2014. Water Distribution System Risk Assessment Method. Procedia Engineering, 89, pp. 355 – 362.
De Corte, A. and Sörensen, K., 2014. HydroGen : an artificial water distribution network generator. Water resources management, 28 ( 2 ), pp. 333 – 350.
Diao, K., Sweet apple, C., Farmani, R., Fu, G., Ward, S. and Butler, D., 2016. Global resilience analysis of water distribution systems. Water Research, 106, pp. 383 – 393.
European Environment Agency, 2017. Water Stress. [online]. Available at < http://www.eea.europa.eu/themes/water/wise-help-centre/glossary-definitions/water-stresshttp://www.eea.europa.eu/themes/water/wise-help-centre/glossary-definitions/water-stress > [accessed 23rd March 2017].
Georgescu, A.M., Georgescu, S.C., Cosoiu, C.I., Hasegan, L., Anton, A. and Bucur, D.M., 2015 a. EPANET simulation of control methods for centrifugal pumps operating under variable system demand. Procedia Engineering, 119, pp. 1012 – 1019.
Georgescu, S.C., Georgescu, A.M., Madularea, R.A., Piraianu, V.F., Anton, A. and Dunca, G., 2015 b. Numerical model of a medium-sized municipal water distribution system located in Romania. Procedia Engineering, 119, pp. 660 – 668.
Gheisi, A. and Naser, G., 2014. Water distribution system reliability under simultaneous multicomponent failure scenario. Journal of American Water Works Association, 106 (7), pp. E319 – E326.
Hardy, J.T., 2003. Climate change: causes, effects, and solutions. Chichester: John Wiley & Sons.
Intergovernmental Panel on Climate Change, 2015. Analysing regional aspects of climate change and water resources. [online]. Available at < https://www.ipcc.ch/pdf/technical-papers/ccw/chapter5.pdfhttps://www.ipcc.ch/pdf/technical-papers/ccw/chapter5.pdf > [accessed 24th March 2017].
Johansson, J., Hassel, H. and Zio, E., 2013. Reliability and vulnerability analyses of critical infrastructures: comparing two approaches in the context of power systems. Reliability Engineering & System Safety, 120, pp.27-38.
Meyer, T. and Reniers, G., 2016. Engineering Risk Management. Berlin: Walter de Gruyter GmbH & Co KG.
Mugume, S.N., Gomez, D.E., Fu, G., Farmani, R. and Butler, D., 2015. A global analysis approach for investigating structural resilience in urban drainage systems. Water Research, 81, 15-26.
Muranho, J., Ferreira, A., Sousa, J., Gomes, A. and Marques, A.S., 2014. Technical performance evaluation of water distribution networks based on EPANET. Procedia Engineering, 70, pp.1201-1210.
Pond, K. and Pedley, S., 2016. Water and Environmental Health In Battersby, S. (ed.) Clay’s Handbook of Environmental Health. Abingdon: Routledge.
Population Institute, 2010. Population and Water. [online]. Available at https://www.populationinstitute.org/external/files/Fact_Sheets/Water_and_population.pdf%20https://www.populationinstitute.org/external/files/Fact_Sheets/Water_and_population.pdf [accessed 24th March 2017].
Prasad, T.D. and Park, N.S., 2004. Multiobjective genetic algorithms for design of water distribution networks. Journal of Water Resources Planning and Management, 130(1), pp.73-82.
Ramana, G.V., Sudheer, C.V. and Rajasekhar, B., 2015. Network Analysis of Water Distribution System in Rural Areas using EPANET. Procedia Engineering, 119, pp.496-505.
Rossman, L.A., 2000. EPANET 2 USERS MANUAL Cincinnati: Water Supply and Water Resources Division National Risk Management Research Laboratory.
Sayyed, M.A., Gupta, R. and Tanyimboh, T.T., 2014. Modelling pressure deficient water distribution networks in EPANET. Procedia Engineering, 89, pp.626-631.
United Nations, 2014. World Urbanization Prospects. New York: UN.
Vasan, A. and Simonovic, S.P., 2010. Optimization of water distribution network design using differential evolution. Journal of Water Resources Planning and Management, 136(2), pp.279-287