*5.1. Scenario* 20% − 1*P*

Scenario 20% − 1*P* simulates rainfall using Seattle's April 2020 precipitation data (1*P*), and 20% of agents (403 of 2016 total agents) are initialized as prosumers. The time series plots of precipitation, irrigation demands and volume of traded rainwater pumped into the network are shown in Figure 5. The simulated horizon includes six distinct rainfall events of varying volumes, followed by a reduction in immediate irrigation demands. The reduction in irrigation demands represents that consumers do not exert irrigation demands within 24 h of a rainfall event. Traded rainwater injections into the reclaimed water network spike after this 24 h period. The highest peaks in irrigation demand each day correspond with the irrigation patterns shown in Figure 3, peaking at hour 19 (or 7:00 p.m.) each day. A total of 525 m<sup>3</sup> of harvested rainwater are pumped into the system during the simulation, which is

the equivalent of the daily water demand exerted by 141 consumer households (8.7% of consumers). The volume of rainwater that is traded is a small fraction (less than 1%) of the total volume of water consumed, as shown in Table 3. The flows of water produced at the treatment plant and consumed at nodes for Scenario 20% − 1*P* are simulated using EPANET (Figure 6), demonstrating that the network satisfies exerted demands without significant excess production; the difference in water produced and water consumed is 7% of the water consumed (Table 3). For this scenario, six of the nine pumps are turned on to meet demands. The centralized system maintains a minimum production volume when consumer demands are zero to meet the constant demand of 0.0079 m3/s (or 20,477 m3 over the one-month period).

The energy consumed for system-level pumping, reclaimed water treatment, and prosumer pumping for Scenario 20% − 1*P* are calculated and compared with the energy required for Scenario 0% − 1*P* (no prosumers) in Table 3 to allow for the examination of energy savings between scenarios with and without rainwater trading. The energy consumed by prosumers for household-level pumping increases by 41 kWh when 20% of households function as prosumers, compared with Scenario 0% − 1*P*. Residential demands are 20% lower in Scenario 20% − 1*P*, due to the number of consumers that switch to prosumers. The increase in energy for household pumping corresponds to a decrease in energy consumed by system-level pumping and treatment. There is a decrease of 2409 kWh in energy consumed by system-level pumps for Scenario 20% − 1*P*, and a total reduction in energy consumption of 11% when compared with Scenario 0% − 1*P*. Unit energy consumed is calculated as the total energy required per unit volume of water produced by both centralized and decentralized processes (Table 3). Unit energy provides an assessment of the energy efficiency of the system. The unit energy for Scenarios 20% − <sup>1</sup>*<sup>P</sup>* and 0% − <sup>1</sup>*<sup>P</sup>* are the same value (0.37 kWh/m3), and the the addition of 403 prosumers to the network does not impact energy efficiency of meeting demands.

**Figure 5.** Precipitation, irrigation demand volume, and traded rainwater volume for Scenario 20% − 1*P*.

Pressure is affected by reductions in consumer demands and the injection of water at terminal nodes through household-level pumping. The maximum pressure in the network occurs when no demands are exerted and is the same value for Scenarios 0% − 1*P* and 20% − 1*P*. As shown in Table 3, the minimum pressure when 20% of households are prosumers is slightly increased, compared to Scenario 0% − 1*P*. The distribution of pressures at a time step with low pressures is shown in Figure 7. The time step shown is 9 p.m. on a day that is preceded by 24 h without rainfall, and pressures remain

at or near the minimum (7 m). In the central area of the city, elevations cover a 30 m range, and the pressures are around 20 m at nodes that are located at high elevations. The southern section of the network is at a lower elevation, and pressures remain in the range of 25–35 m during this period of relatively low pressure.

**Figure 6.** EPANET output reports flow of water produced by the treatment facility and flow of water consumed at nodes for Scenario 20% − 1*P*.


**Table 3.** Metrics reported for Scenarios 0% − 1*P* and 20% − 1*P*.

Water age is calculated for Scenarios 20% − 1*P* and 0% − 1*P* using Equation (14), calculated over all irrigation nodes, and is reported to explore water quality. It is expected that the water age of Scenario 20% − 1*P* would be higher than the water age of Scenario 0% − 1*P*, because the injection of water at households may increase the residence time of water in the system, and there are fewer agents consuming water in the network. The water age of Scenario 20% − 1*P* is marginally less than the water age of Scenario 0% − 1*P* (a difference of less than 1 h). This difference may be due to the process of calculation. The water age is calculated only at consumer nodes, and there are fewer households acting as consumers in Scenario 20% − 1*P*, leading to a marginal reduction in water age. In addition, the age of water entering the system due to household-level pumping is initialized at zero hours, which does not account for the time that the water resides in the household-level rainwater harvesting tank.

**Figure 7.** Lowest nodal pressures for Scenario 20% − 1*P* at 9:00 p.m. on a day with no rainfall in the previous 24 h.

#### *5.2. Performance Analysis across All Scenarios*

The total volume of traded rainwater, total number of trades, and percentage of irrigation demand met for each of the 126 scenarios (six levels of precipitation and 21 levels of prosumers) are shown in Figure 8. For all scenarios where no agents are prosumers (0%) or all households are prosumers (100%), no trades occur because of the homogeneity of agents. For all other scenarios, an increase in rainfall volume corresponds to an increase in volumes of trades (Figure 8a) and number of trades (Figure 8b). During higher precipitation volume scenarios, prosumer agents can harvest higher volumes of rainwater, which allows some consumer agents to satisfy demands through trading. For higher precipitation, the peaks in volume and number of trades correspond with lower percentages of prosumer agents. During scenarios with precipitation volume 1*P*, for example, the maximum volume of traded rainwater corresponds with a prosumer ratio of 80%, compared to 50% for precipitation volume 4*P*. This is because for lower rainfall depths, a higher number of prosumers are needed to participate in the market to offset the demand exerted by a consumer. The highest number of trades occur for scenarios with precipitation volume 1*P*. Consumer agents buy rainwater from multiple prosumers at each time step to meet demands, leading to a high number of trades (Figure 8b). At low precipitation depth, 0.5*P*, the number of trades is relatively low, because prosumer agents are unable to harvest higher volumes of rainwater, resulting in reduced ability to trade. The volume of rainwater that is traded decreases for higher numbers of prosumer agents because fewer agents are consumers

to exert demands. The system does not meet total irrigation demands for any of the 126 scenarios (Figure 8c), however, because irrigation demands of consumers are substantially higher than harvested rainwater volumes. Across all precipitation volumes, the highest percentage of demand that is met through trading occurs when 95% of agents are prosumers.

(**c**) Percent of consumer demand met via trades.

**Figure 8.** Total volume of traded rainwater (m3), total number of trades, and total percentage of irrigation demand satisfied by traded rainwater across 126 scenarios of varying rainfall depth and percentage of prosumer agents.

EPANET simulations were used to evaluate energy consumption, pressure, and water age. The amount of energy consumed by household-level pumping (Figure 9a) follows the same pattern as the volume of traded rainwater (Figure 8a) with the highest consumption of energy at high rainfall depths and around 50% prosumers. Scenarios with lower percentages of prosumer agents and low rainfall volumes require more system-level energy consumption (Figure 9b). System-level energy is orders of magnitude greater than energy consumed by household-level pumping, and there is a large reduction in system-level energy requirements for higher numbers of prosumers. This trend emerges because prosumer agents do not irrigate, which reduces the energy requirements of pumping from decentralized locations. Energy consumed for treatment is high for this system, approximately twice the energy required for pumping. Treating wastewater to non-potable standards is an energy-intensive activity, and these numbers reflect that cost. In this research, we assume that the volume of wastewater is treated to match the unmet demands in the systems, and the energy cost of treating excess wastewater that is not needed for reuse is not included in this framework. However, wastewater that is released to the environment or used for other recycling purposes would also need to be treated, and a holistic assessment of the interconnections between water, wastewater, and reclaimed water systems may use an alternative approach to holistically account for energy costs. Based on the sum of energy requirements for the smart water grid system (Figure 9d), a higher number of prosumers leads to higher savings in energy.

**Figure 9.** Energy consumption for (**a**) prosumers for pumping water at households, (**b**) system-level pumping, (**c**) treatment of water at the treatment plant, and (**d**) the sum of energy consumption for prosumers, system-level pumping, and water treatment.

The system's unit energy is calculated as the energy consumed by three processes (household-level pumping, system-level pumping, and treatment) per unit volume of water produced by the centralized system and prosumer pumping (Figure 10). Unit energy is used to represent the efficiency of the system in meeting demands. For scenarios of high percentages of prosumers and high precipitation depths, the water contributed by prosumers reduces the amount of water required by the centralized system, leading to higher energy efficiency. For example, unit energy generally increases across 1*P* scenarios, which corresponds with the reduction in treatment and pumping energy shown in Figure 9b,c. Household-level pumps inject water in the network at peak demand times, which offsets the need to use the additional pumps that operate in parallel to the main pump. As a result, the number of pumps that operate to provide water from the centralized system decreases with increasing numbers of prosumers (nine pumps are needed for 0–5% prosumers; seven pumps: 10–15%; six pumps: 20–25%; five pumps: 30–40%; four pumps: 45–60%; three pumps: 65–80%; two pumps: 85–95%; one pump: 100%). Further, pumping water from terminal nodes in the network requires less energy than pumping from the centralized treatment plant, as there is less head loss to overcome when the water is pumped from near-by terminal nodes.

Unit energy does not increase monotonically across the 1*P* scenarios, however, because of the infrastructure complexities of water production. For some 1*P* scenarios, water production exceeds demands on the centralized system by up to 18%, while in others, water production drops to 91% of the demand exerted on the centralized system (that is, total demand minus the demands that are met by household-level pumping). In cases where the water demanded exceeds the water produced by the centralized system, the water storage tanks meet the remaining demand because they are initialized at full capacity. At 80% prosumers, the system reaches a minimum unit energy, and, subsequently, the energy required per unit volume increases with increasing percentages of prosumers. This trend mirrors the change in volume of traded rainwater across scenarios of increasing numbers of prosumers, shown in Figure 8a, which reaches a peak at 80% prosumers for the 1*P* scenario. When consumers comprise less than 20% of agents, they demand less water than prosumers produce when tanks are full. Because low volumes of water are traded and the bulk of demand is at the constant demand, which is met by the centralized system, the system requires higher unit energy. Higher precipitation depths (2*P*, 3*P*, 4*P*, and 5*P* scenarios) lead to improved energy efficiency because prosumers can produce more water to offset demands. Increasing the volume of water that can be provided by prosumers increases benefits to both water and energy savings through the smart water grid.

**Figure 10.** Energy consumed per unit volume of water produced. Energy is calculated as the sum of all three energy expenditures: household-level pumping, centralized pumping, and treatment. Produced water is calculated as the sum of water produced by the centralized system and the water produced by prosumer agents.

The minimum and maximum pressure across all consumer irrigation nodes and over all time steps are reported for each scenario. The minimum pressure across the scenarios varies between 5.0 and 30 m of head (Figure 11), while the maximum pressure is approximately the same at around 50 m for all scenarios. The minimum pressure is low at high numbers of consumers (low percentage of prosumers). Scenarios where the minimum pressure values fall below 7 m (approximately 10 psi) may be considered as infeasible because the pressure is not high enough to meet irrigation purposes. For 1*P* rainfall scenarios, scenarios are infeasible until the percentage of prosumer agents reaches around 30%. When the number of prosumers is lower than 30%, consumers require a large volume of water from the centralized system, and pressures in the central part of the system drop to values less than 7 m. With higher precipitation depths, the amount of water that is provided by prosumer agents increases, resulting in relatively higher minimum pressure values. For higher precipitation scenarios, prosumers

contribute high volumes of water, leading to increasing pressure. For example, for 5*P* rainfall scenarios, approximately 15% of agents need to be prosumers to ensure a feasible system.

**Figure 11.** Minimum head (m) across consumer nodes for all scenarios.

As the number of prosumers increases, there are benefits in energy savings and meeting pressure requirements, as shown above. There is, however, an expected drop in water quality based on the residence time of water in the network. As the system has intermittent consumption for irrigation purposes, water age increases in scenarios with high precipitation values and high percentages of prosumers (Figure 12). Water age values represent the average number of hours exceeding the water age requirement of 48 h, and this number is between 20 and 30 h when the percentage of prosumers is less than 80%. The effect on water age does not grow significantly until the percentage of prosumers reaches 80%, and water age increases dramatically with additional prosumers. Tradeoffs among water age, energy consumption, and pressure may govern how a water micro-trading market should be designed. Results show for 1*P* scenarios, that water saving is at a maximum at 80%; unit energy is minimum at 80%; pressure requirements constrain the network to function only if 30% or more households join as prosumers; water age requirements may constrain the percentage of prosumers to less than 80%.

**Figure 12.** Water age calculated for all scenarios using Equation (14).

## **6. Discussion**

This study proposes and tests the hydraulic feasibility of a smart water grid for micro-trading rainwater through a peer-to-peer non-potable water market that allows residential households to capture, use, sell, and buy rainwater within a network of water users. In this research, we explore the impact of the depth of rainfall and the distribution of consumers and prosumers on the performance metrics that are used to evaluate the hydraulic feasibility of the smart water grid. In related research, an agent-based modeling framework was developed to explore how the numbers of prosumers and consumers affect performance of a peer-to-peer household-level energy trading market, and results demonstrated that the presence of too many prosumers in the market led to market inefficiencies [8]. In the smart water grid, however, the volume of water that is required by consumers for irrigation is much higher than the volume of water that is produced by prosumers. Prosumers could not completely satisfy consumer demands for any of the simulated scenarios, and production from the centralized system was required to meet demands.

The volume of water that is produced by prosumers drives the performance of the smart water grid, with respect to both water and energy savings. The total volume of traded water increases and the energy required to pump demands decreases for scenarios with higher numbers of prosumers and higher rainfall depths, leading to a more energy efficient system. The energy requirements at households to pump water from rainwater tanks is lower than the energy required at the system level to pump the same volume of water from the water treatment plant. Pumping water from the central treatment plant requires the operation of extra parallel pumps, which are not needed when prosumers contribute water to the system. In addition, water that is pumped into the network at terminal nodes by prosumers does not need to overcome headlosses or elevation losses when consumer nodes are located nearby. Energy savings are also associated with treating smaller volumes of wastewater to nonpotable standards. In this model, the efficiencies of household pumps and systems were assumed to be equal (75%). Household pumps, however, may more realistically have lower efficiency than large pumps, which would change the analysis of energy consumption. The model developed in this research does not account for energy requirements of onsite treatment that could be required at prosumer households to treat rainwater. It is expected, however, that treatment of rainwater to meet nonpotable standards would require much less energy than treatment of wastewater. Pressure and water quality constraints are also explored in this research, as they are affected by increased trading and show tradeoffs based on the number of prosumers. For the simulations conducted in this research, consumer and prosumer agents are assigned randomly at nodes across the network, and the results are specific to one random realization. Further research can explore how clustering of consumer or prosumer agents at nodes in the network could affect pressure, energy, and water age through multiple realizations of initializing consumer and prosumer agents.

In this research, rainfall and evapotranspiration the data that are used to simulate demands are from the Seattle, WA, USA area, and we explore how higher precipitation can lead to a more efficient market. The modeling framework presented in this manuscript uses the theoretical outdoor water demand model, which may overestimate the amount of water required by households. Other climates may lead to differences in rainwater exchanges, and new methods for estimating irrigation may be needed to more accurately represent household behaviors.
