*4.1. Basic Characteristics*

Following the methodology, an analysis for flows and pressures is necessary for energy consideration in the network based on hydraulic simulations. These simulations have been run with the software EPANET.

The model of the network developed by means of the software EPANET, has been run for each day along one year. In this case, these calculations have been repeated 20, 40 and 60 times with different scenarios represented. Nevertheless, comparing these simulations, the variability obtained when the flow in the main line is compared to the average flow is smaller than 5%. As this deviation remains similar, no more repetitions are considered.

This methodology has been calibrated in other networks by the authors. The calibration has been performed with measured flow every five minutes. The results have been satisfactory with Nash-Sutcliffe index upper to 0.40, root relative squared mean error below 0.7 and percent bias below 5%, as indicated in [47].

Figures 12 and 13 depict the topology of the network to be considered and analyzed in further sections.

**Figure 12.** Identification of pipes in the irrigation network.

**Figure 13.** Identification of hydrants in the irrigation network.

### *4.2. Flows in the Network*

Flow and pressure have been obtained along the time, based on the historical series of records registered between 2003 and 2014, in any line of the system, according to the irrigation trends. These time series of data collected in those 12 years (17,808 records), flow in the main line (see Figure 12, line 1) and hydrant 201 (see Figure 13, H201) are depicted in Figure 14.

**Figure 14.** Flow in the main line (pipe 1) along the year (**a**); Flow and pressure variation in the hydrant (H201) over time (**b**).

The frequency histogram (Figure 15) displays the large variability of flows along the year. Hence, irrigation networks behave in a different way than drinking systems: monthly seasonal ratios range between 0.8 and 1.2 in drinking networks (except for touristic cities) and its variability of flows during the day varies between 0.7 and 1.5 of the average value. Opposite to this, the flow seasonality factor in irrigation systems is much larger than in drinking systems. In the case of citrus, seasonality factor varies between 0.14 and 2.36 times relative to the annual average consumption volume. According to this, the estimated variability in this network case study ranges between 0.1 and 2.54 times the average flow.

Additionally, there is a very high frequency of very low flows (Figure 15). Flows below 0.05 m3/s (25% of the maximum flow rate) arise up to 80% times in the main line of the network. These small flows will become of utmost importance to be used for energy recovery.

**Figure 15.** Histogram of flow in the main line.

### *4.3. Water-Energy Nexus Estimation*

This section analyzes the estimation of energy dissipated in the network as a result of friction losses. Figure 16 shows the variation of the energy footprint based on time. The network is working 5943 h during of the year. Figure 16 shows the energy footprint during the distribution of flows in the water network. As shown in the histogram, 99.7% of the time the network has an energy footprint below 2 kWh/m3. The maximum value obtained is 2.87 kWh/m<sup>3</sup> for a July day. However, 58.5% of the time the network has an energy footprint below 0.1 kWh/m3.

**Figure 16.** Network energy footprint of water.

### *4.4. Theoretical Recoverable Energy*

If the results are analyzed in irrigation points, the total theoretical recoverable energy is 188.23 MWh/year (*i.e.*, 68.7% of the total energy supplied to the network). In these nodes, the theoretical coefficient of recovery (*CRT*) is equal to one, as *ERT* is equal to *ETA*.

Figure 17 shows a detail of instantaneous power along data registered for the month of July for the analyzed time series, and the distribution of instant power frequencies over time for an irrigation point. In these points, the frequency at which the value of instantaneous power appears is practically constant because the consumption flow is uniform and only pressure varies due to the use of pressure-compensating drippers.

As an example, in irrigation point 303, the annual operating time is 2957 h. The instantaneous power oscillates between 9.96 kW and 11.64 kW. The maximum power occurs 44.2% of time, and the theoretical total energy is 33.80 MWh/year (Figure 17).

In the case of hydrants, the result is similar where the sum of the theoretical recoverable energy is 178.1 MWh/year. Figure 18 shows analogous results to those exposed in the irrigation points. Particularly, a maximum instantaneous power of 4.64 kW is achieved in hydrant H201, with an annual operating time of 1460 h and total energy of 1.59 MWh/year. The average weighted coefficient of recovery in this hydrant is 0.68 (*i.e.*, 9.68% of the total energy could be recovered if turbines had 100% efficiency). The maximum recovery occurs in the hydrant H045 with 16.12 MWh/year, with a recovery rate of 0.83 (Figure 18).

The values of theoretical energy recoverable in all hydrants are detailed in Table 1, as well as their recovery coefficients. The theoretical maximum recoverable energy is obtained in hydrant H042 with a total energy of 33.73 MWh/year, and a coefficient of recovery of 0.80. The theoretical energy ranges between 0.01 (H056) and 33.73 MWh/year. The recovery coefficient ranges between 0.14 (H055) and 0.84 (H053). The weighted average recovery coefficient is 0.75.

**Figure 17.** Potential Power in the irrigation point 303.

**Figure 18.** Potential Power in hydrant H201.


**Table 1.** Theoretical energy recoverable in hydrants on the irrigation network.

The line that presents the maximum recoverable energy is depicted in Figure 19 and Table 2. This condition is set on line 38, with maximum recoverable energy of 89.99 MWh/year and an average weighted recovery rate of 0.64. The maximum instantaneous power is 63.7 kW. The histogram presented in Figure 19 shows that during 918 h of the operating time (17.1%), the instantaneous power arises up to 10 kW.

Table 2 shows that the maximum recoverable energy is obtained in line 38 with total energy of 89.99 MWh/year and a coefficient of recovery 0.64. The estimated energy (*ERT*) ranges between 0.12 (line 21) and 89.99 MWh/year, the range of recovery coefficient can be found between 0.15 (line 74) and 0.84 (line 58) and the weighted average coefficient is 0.48.

The pairs of flow, *Qi*, and head, *Hi*, defined in Equation (11) for any point of the network are crucial to determine energetic aspects. With these data (flow and head), the estimated area of operation of the future selected machine could be determined. This cloud of point pairs is depicted in Figure 20 for an irrigation point, a hydrant and two of the lines with the maximum theoretical recoverable energy.

Figure 20 shows that not all lines have narrow operating point intervals. Line 59 has a large dispersion of operating points in the flow range. Similar circumstances occur in hydrant H201 with a wide range of flow, making the choice of a unique turbine difficult. In the case of recovery in irrigation points, the flow is constant with an interval of pressure according to the demand of the network. This becomes an additional advantage in which the performance of the chosen machine could be easily optimized.

**Figure 19.** Potential Power in line 38.

**Table 2.** Estimated energy recoverable in lines on the irrigation network.



**Table 2.** *Cont.*

**Figure 20.** Representation of flow *versus* head for ideal turbine characteristics in irrigation point, hydrant and lines 38 and 55.
