**2. Methodology**

This paper discusses how poorly planned network expansions can lead from CWS to IWS. We propose the use of the theoretical maximum flow as an indicator for evaluating the network capacity, and then analyzing its relationship with intermittent supply.

Generally, the capacity of a water distribution network is considered a qualitative concept, which is usually identified from user complaints of pressure reduction [26].

We consider that network capacity represents the maximum demand (or flow) that can be met while maintaining suitable pressures throughout the network, and strictly ensuring the minimum pressure required at the node with the lowest pressure. When this flow does not cover the demand of the population, the network has insufficient capacity. Given this scenario, the network responds by reducing pressure at nodes to achieve total user demand. This situation may threaten the continuity of water supply. Even though it is possible to use a PDD (pressure driven demand) analysis, in low pressure networks, a more conservative and, thus, safer design is obtained by making use of mathematical models using demand driven analysis (DDA), and representing its capacity deficiency as a flow magnitude, since negative pressures have no physical meaning in cases of deficient network capacity.

We propose the use of the theoretical maximum flow calculated with the pressure-restricted setting curve, explained later. To evaluate the capacity of a system network with IWS, the maximum theoretical flow is compared with the maximum flow required by the population in continuous supply. It is thus possible to establish the potential of converting CWS into IWS. Intermittent water supply is usually caused by the extension of the distribution network beyond its hydraulic capacity [27].

Therefore, a method is also proposed to increase the capacity of the network, as a part of a project for gradual transition towards CWS, while taking into account that the system suffers insufficient funding.

It is common to gradually carry out the process of expanding the network capacity with more or less localized interventions on its components, so as not to endanger the service and ensure a greater lifespan for the infrastructure [25].

Another important restriction on some systems with IWS is related to the economic constraints of the water company. Therefore, we propose a gradual expansion of capacity divided into stages, in which a schedule is defined for every stage (the optimal option being sought in each of these stages). Taking advantage of improvements in network capacity, CWS gradually spreads until the entire network is covered.

When a network requires expansion, it is common practice to use optimization techniques to find a solution with lower costs and satisfactory pressures. However, these processes tend to define the overall set of pipes regardless the necessary actions associated with stage-divided projects.

In this paper, the use of the theoretical maximum flow reduces the search space to an area equal to the number of pipes evaluated and multiplied by the number of candidate diameters and number of stages.

This advantage enables us to propose the strategic replacement of pipes in a context of economic scarcity by a greedy algorithm that enables the optimal option in each of the stages to be selected—in an attempt to reach an optimal general solution. A schedule of the stages for modifying the network is defined in this way, and the result is a gradual and more efficient transition to CWS.

As the influence of each of the pipes in the total capacity of the network is known, another advantage of the proposed method is the possibility of detecting bottlenecks in the network.
