Volume-Driven and Flow Control Approach to Optimizing Equity in Intermittent Water Supply Systems ^†

Abstract

Over 1.3 billion people worldwide are serviced by intermittent water supply (IWS) systems, which are characterized by their inability to provide continuous water to consumers for 24 h a day. Consumers in IWS systems often rely on private storage tanks as a coping mechanism during periods without water access. Although these tanks can improve supply reliability, they also worsen existing inequity in water access, where some consumers have greater access to water than others. This research introduces a simulation–optimization framework that integrates volume-driven demand into hydraulic simulations in order to account for the utilization of private storage tanks in IWS systems. Bayesian optimization is utilized to determine a flow control schedule that maximizes the local supply and global equity amongst consumers. The proposed approach is applied to an IWS system, where we explore the mechanisms through which the disparity in hydraulic conditions across the network creates inequity in water access. The results reveal a hierarchy in supply amongst the consumers that dictates the degree to which consumers have access to water. While flow controls can offset some of the global disparities, the local supply hierarchy is maintained through micro-level consumer behavior that a partially controlled system cannot fully override. This work underscores the importance of the interplay between local consumer behavior and global supply equity and provides insights into the mechanisms behind supply inequity.

1. Introduction

Intermittent water supply (IWS) systems, characterized by their failure to provide round-the-clock water access, are prevalent around the world, particularly in low and medium-income countries [1]. To cope with the gaps in water supply, consumers within the IWS systems frequently install private storage tanks, enhancing water availability during hours of no supply. However, these local storage tanks exacerbate the disparities in water access among consumers due to variability in local pressure conditions, leading to unequal water availability among consumers. The behavior observed in IWS systems reveals that consumers in hydraulically advantageous positions, such as in locations with lower elevations or that are closer to the water sources, enjoy better access to the water supply. Hence, this enhanced access for some leads to reduced access for others, manifesting as a global disparity in water supply availability [2].

In this context, our research adopts a model-based strategy aimed at (1) investigating how varying hydraulic conditions contribute to local and global disparities in water supply, thereby offering insights and strategic guidance on managing IWS systems, and (2) evaluating how equitable distribution of water can be achieved among consumers by strategically regulating the water flow to different areas of an IWS.

2. Methods

2.1. Problem Formulation

The distinct hydraulic characteristics of IWS systems permit certain consumers to withdraw water exceeding their immediate demand, consequently diminishing water availability for others during supply periods and hindering their capacity to accumulate enough water for times with no supply. We propose a simulation–optimization approach that accounts for the unique dynamics of IWS systems and designs an operating strategy that limits the uneven water distribution among consumers. This is achieved by scheduling optimal flow control valve (FCV) settings that maximize global supply equity between consumers.

2.2. Modeling IWS Systems

Traditional continuous water supply (CWS) demand models, including demand-driven analysis (DDA) and pressure-driven analysis (PDA), only account for the immediate water consumption and overlook the significant aspect of water being discharged into or withdrawn from local storage tanks. This oversight misrepresents the true timing and volume of consumer demand, leading to discrepancies in demand modeling for IWS systems. To address these challenges, we apply the volume-driven demand (VDD) model, which was introduced previously as a technique for modeling IWS systems [3]. This approach limits the flow from the system to the consumer node solely based on the volume of the local storage tank. Implementing VDD involves transforming a CWS model into an IWS model by augmenting each consumer node with a check valve, a storage tank, and a pressure-driven discharge node.

2.3. Performance Metrics

The performance of the management strategy is assessed using two metrics: (1) supply ratio (SR), which quantifies the extent to which the local demand of each consumer is met, and (2) supply equity (SE), which aggregates the supply ratios of all consumers into a single measure that reflects the global level of disparity in water access among consumers. Both SR and SE range between 0 and 1, where 1 indicates perfect performance and 0 indicates worst performance.

2.4. Optimization Approach

The overall strategy of the optimization approach involves setting spatiotemporal flow restrictions within the system to curb excessive water use by consumers who are in hydraulically advantageous positions. By doing so, it ensures that those in less favorable conditions receive better access to water, thereby enhancing global supply equity. We assume that real-time water level data from local storage tanks is not necessary. Instead, the operational schedule for each FCV is predetermined by the control model based on a specified operating horizon and a forecasted schedule for intermittent water supply. This approach simplifies the system’s management by relying on predictive modeling rather than continuous monitoring, focusing on optimizing water distribution efficiency within the given constraints of supply variability and local storage.

The hydraulic simulation of the IWS system represents a computational challenge, due to the additional complexity introduced by incorporating local storage tanks and control valves. To enhance the computational feasibility of this simulation-optimization problem, Bayesian optimization (BO) is employed [4]. This approach optimizes the objective while minimizing the number of required simulations, thereby reducing the overall computational load. BO operates by training a surrogate model to map the input-output relationships. This model serves as an approximation of the actual simulation model, allowing for a more efficient exploration of the solution space by predicting outcomes without the need for exhaustive simulations.

3. Results

We demonstrate our proposed methodology using a branched network with 161 consumers that are supplied through pumping from a single reservoir located in the center of the network. The network is divided into six zones, each connected to the transmission main via FCV. To simulate intermittent supply conditions, a supply schedule was implemented where the source pumps operate only during the first 8 h of a 24 h time frame, remaining inactive for the remaining 16 h.

Figure 1 displays the tank level dynamics at the individual consumers during the day without any flow control measures. The results show a diverse and staggered pattern in tank dynamics. Overall, we observe that consumers with favorable hydraulic conditions, in locations with lower elevations and that are closer to the source, fill their tanks first and reach full capacity ahead of others (blue lines). These consumers take precedence over the others and fill their tanks to the maximum levels, while others experience slower inflow rates. Once these advantaged consumers’ tanks are full, those next in the hierarchy (yellow lines) then begin to see an increase in their tank inflow rates, continuing until they too achieve maximum storage capacity. This pattern repeats itself, where tanks are repeatedly filled as long as there is available supply from the source, reinforcing the hierarchical distribution based on hydraulic advantage. In contrast, consumers with less favorable conditions (red lines) are left waiting until those above them in the hierarchy have filled their tanks. Even when they do receive water, their inflow rates are often curtailed by the ongoing refilling of tanks by those higher up in the hierarchy. As a consequence, these disadvantaged consumers struggle to accumulate sufficient reserves to meet their needs outside of the supply periods, highlighting the need for equitable distribution strategies.

Figure 2 shows the improvement in the supply ratio and supply equity across the transmission main (Z-0) and six zones following the implementation of flow control measures. The radial axes quantify SR and SE, with 1 symbolizing an optimal outcome and 0 the opposite. The comparative analysis of the baseline scenario (blue) against the optimized scenario (red) demonstrates a notable improvement, with SR increasing from 0.79 to 0.87 and SE increasing from 0.61 to 0.78. This improvement predominantly benefits the hydraulically disadvantaged zones (4–6), achieved by strategically reducing water flow to the hydraulically superior zones (1–3) at certain times. While zones 1–3 experience a slight reduction in supply, this flow adjustment considerably enhances water availability in zones 4–6, illustrating the effectiveness of flow control measures in promoting a more balanced and equitable distribution of water resources across the network.

4. Conclusions

This study emphasizes the potential of simulation–optimization models to devise fair control mechanisms within IWS frameworks, identifies the origins of inequality, and highlights key elements that exacerbate disparities. The application of the VDD approach revealed disparities within the network. This is particularly evident in the way private storage tanks create a layered supply structure among consumers, establishing a supply hierarchy. This research underscores the limitations of macro-level controls to achieve a more equitable distribution of water at the level of individual consumers. Overall, while managing IWS systems is inherently complex, requiring interventions that span social, political, economic, and technical dimensions, accurate models remain indispensable for guiding decisions [5]. Therefore, it is crucial that these models evolve beyond the paradigms of conventional CWS systems, continually being refined to better support the goal of improving service to all IWS system consumers.