# Pump-as-Turbine Selection Methodology for Energy Recovery in Irrigation Networks: Minimising the Payback Period

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}ha

^{−1}. Renewable energy will become increasingly important in the agriculture sector, to reduce both water costs and the contribution to climate change. PATs represent an attractive technology that can help achieve such goals.

## 1. Introduction

^{−1}, increasing the energy recovery by 141% and 184% when comparing to constant rotational speed PATs [24]. Finally, the use of PATs for energy recovery in irrigation networks was also studied in an area of 68 ha in Portugal. The potential estimated to be recovered was 2.12 MWh [25].

## 2. Materials and Methods

#### 2.1. Methodology

#### 2.1.1. Location of Excess Pressure Points and Calculation of Downstream Open/Closed Hydrants Combinations

#### 2.1.2. Open Hydrant Probability Calculation

^{−1}month

^{−1}), was obtained, with i referring to the hydrant and j to the month.

^{−1}), and the monthly water availability, ${T}_{ij}^{\prime}$ (hours month

^{−1}) for each hydrant i in each month j. These were calculated following Equations (4) and (5), respectively. Finally, $hour{s}_{i}$ refers to the daily water availability (hours) per hydrant and $day{s}_{j}$ (days month

^{−1}) to the number of days in the month j. ${q}_{max}$ is the design flow allowed per unit of irrigated area.

#### 2.1.3. Monthly Characterisation of the Network: Mass Probability Function, ${p}_{X}\left(x\right)$ Calculation

#### 2.1.4. PAT Operating Conditions Analysis

- (i)
- $if\hspace{0.17em}{Q}_{lm}\le {Q}_{lMAX}\left\{\begin{array}{l}{Q}_{PAT}={Q}_{lm}\\ {Q}_{lmBP}=0\end{array}\right\}$
- (ii)
- $if\hspace{0.17em}{Q}_{lm}>{Q}_{lMAX}\left\{\begin{array}{l}{Q}_{PAT}={Q}_{lmPAT}\\ {Q}_{lmBP}={Q}_{lm}-{Q}_{lmPAT}\end{array}\right\}$

#### 2.1.5. Economic Viability

#### 2.2. Study Area

## 3. Results

#### 3.1. Location of Excess Pressure Areas and Calculation of Downstream Open/Closed Hydrant Combinations

#### 3.2. Open Hydrant Probability Calculation

#### 3.3. Monthly Characterisation of the Network: Mass Probability Function, ${p}_{X}\left(x\right)$ Calculation

^{−1}, 0–82 l s

^{−1}, 0–179 l s

^{−1}, 0–101 l s

^{−1}and 0–75 l s

^{−1}, respectively. From these results, a distribution of the flows along the irrigation season was obtained, and the monthly behaviour of the network could be characterised by analysing the 12 monthly binomial distributions. The mass probability functions were calculated using Equation (8).

#### 3.4. PAT Operating Conditions Analysis

#### 3.5. Economic Viability

## 4. Discussion

^{−1}ha

^{−1}. This shows that the potential available in this specific network is not large. Previous investigations showed values of 0.65 and 0.08 MWh year

^{−1}ha

^{−1}[22,23]. However, these values cannot be compared, since each index will partially depend on the topography in which the network is built. In addition, previous estimates did not considered both flow variations and turbine efficiency variations.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

$a$ | Random scenario |

$A{R}_{l}$ | Annual revenues generated for the installation designed for the flow l |

$BT$ | Bernoulli Trial |

$C$ | Combinations of downstream open hydrants |

${C}_{PPnl}$ | Total cost for a PAT with n magnetic polar pairs generator installation for the flow l |

$day{s}_{j}$ | Monthly days |

$E{V}_{j}$ | Monthly experimental volumes |

${E}_{lj}$ | Monthly energy recovered in the scenario l |

${H}_{BEP}$ | Best efficiency point head |

${H}_{lmPAT}$ | Head recovered for flow m in scenario l |

$I{N}_{ij}$ | Monthly water requirements per hydrant |

$N$ | Number of simulations |

$n$ | Number of downstream hydrants |

${n}_{lj}$ | Monthly number of repeating times of the flow value l |

${p}_{ij}$ | Monthly open hydrant probability |

${P}_{lm}$ | Power for the scenario produced for the inlet flow m in the scenario l |

${p}_{X}\left(x\right)$ | Mass probability function |

$p\left({q}_{lj}\right)$ | Monthly mass probability function of the flow value l |

${p}_{cw}$ | Percentage of civil works in the total installation cost |

$P{P}_{nl}$ | Payback period for an PAT installation design for the flow l with a generator with n polar pairs |

${q}_{max}$ | Design flow of the network |

${q}_{M}$ | Maximum flow running in the pipe EPP studied |

${q}_{l}$ | Value of the flow in scenario l |

$Q$ | Random variable Flow |

${Q}_{lBEP}$ | BEP flow value in scenario l |

${Q}_{lmPAT}$ | Flow running through the PAT when m flow is demanded in the scenario l |

${R}_{j}$ | Monthly random vector [0-1] |

${r}_{j}$ | Monthly energy tariff |

${{t}^{\prime}}_{ij}$ | Monthly hydrant irrigation time required |

${{T}^{\prime}}_{ij}$ | Monthly hydrant water availability |

${\eta}_{max}$ | Maximum PAT performance |

${\eta}_{lm}$ | Relative performance of the flow value m in the PAT designed for flow value l |

$\gamma $ | Water specific weight |

Sub-indexes | |

$i$ | Hydrant sub-index |

$j$ | Month sub-index |

$l$ | Flow values for main scenarios sub-index |

$m$ | Flow values for relative scenarios sub-index |

$n$ | Generator magnetic polar pair sub-index |

## Appendix A

Civil Works | |||||
---|---|---|---|---|---|

CW.1 | Manual trench excavation (20 × 2 × 1.5 m) | m^{3} | 76 | 49.45 | 3758.20 |

CW.2 | Bypass: Supply + fixing 300 mm ductile iron pipes | lm | 18 | 96.35 | 1734.30 |

CW.3 | Reinforced concrete slab 10 cm | m^{2} | 8 | €16.2 | €129.8 |

CW.4 | Protection House: Concrete blocks (40 × 20 × 10 cm) supply and fixing (4 × 2 × 2.5 m) | m^{2} | 30 | €41.78 | €1253.40 |

CW.5 | Manual backfilling: Same material excavation | m^{3} | 76 | €3.54 | €269.04 |

Total | €7144.78 |

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**Figure 4.**Representation of a potential PAT flow-head curve for a hypothetical site, and working pairs (${Q}_{lmPAT},{H}_{lmPAT})$ for a random flow ${Q}_{lm}$ greater than the maximum ${Q}_{lMAX}$ in the Q-H space.

**Figure 6.**Mass function, $p\left(q\right)$, for the possible flow values in March, April, May, June, July, September and October for EPP 3.

**Figure 8.**Theoretical irrigation volume requirements and experimental irrigation volume requirements for EPP 3.

**Figure 9.**Comparison between the highest energy-producing scenario and the lowest PP scenario in EPP3.

**Table 1.**Monthly open hydrant probability by crops depending on the surface occupied, and total monthly open hydrant finally applied to every hydrant during the irrigation season.

Crop | Surface Percentage | Monthly Open Hydrant Probability (%) | |||||||
---|---|---|---|---|---|---|---|---|---|

March | April | May | June | July | August | September | October | ||

Citrus | 56 | 0.3 | 4.1 | 14.7 | 25.5 | 28.1 | 24.4 | 13.0 | 1.0 |

Maize | 32 | 0.0 | 0.0 | 7.6 | 23.8 | 26.7 | 14.6 | 0.0 | 0.0 |

Cotton | 9 | 0.0 | 0.0 | 1.8 | 6.0 | 7.1 | 4.2 | 0.0 | 0.0 |

Sunflower | 3 | 0.0 | 0.0 | 1.1 | 2.5 | 2.4 | 0.3 | 0.0 | 0.0 |

Total (%) | 100 | 0.3 | 4.1 | 25.2 | 57.8 | 64.3 | 43.5 | 13.0 | 1.0 |

**Table 2.**Summary of the EPPs found, downstream hydrants, number of possible flow values, flow range and monthly and yearly number of Bernoulli Trials run conducted.

EPP | Downstream Hydrants | Flow Values | Q Range (l/s) | Bernoulli Trials | Total Simulations |
---|---|---|---|---|---|

1 | 23 | 8,388,608 | 0–297 | 17,000,000 | 204,000,000 |

2 | 5 | 32 | 0–82 | 15,000 | 180,000 |

3 | 21 | 2,097,152 | 0–179 | 5,000,000 | 60,000,000 |

4 | 26 | 67,108,864 | 0–101 | 140,000,000 | 1,680,000,000 |

5 | 21 | 2,097,152 | 0–75 | 5,000,000 | 60,000,000 |

**Table 3.**Summary of the results obtained for each EPP and for the set, showing the optimal scenario, BEP flow, BEP power of the optimal scenario, number of polar pairs of the electromechanical device, total installation costs, energy recovered in the optimal scenario and its PP.

EPP | Optimal Scenario | BEP Flow (l/s) | BEP Power (kW) | Polar Pairs | Cost (€) | Energy (MWh) | PP (Years) |
---|---|---|---|---|---|---|---|

1 | 2,743,236 | 88 | 9.1 | 1 | 16,438 | 40.8 | 3.5 |

2 | 13 | 39 | 2.9 | 2 | 12,339 | 6.9 | 15.8 |

3 | 631,784 | 54 | 5.8 | 2 | 14,207 | 29.5 | 4.2 |

4 | 30,122,847 | 46 | 4.5 | 2 | 13,352 | 11.1 | 10.6 |

5 | 1,051,433 | 36 | 2.8 | 2 | 12,278 | 5.6 | 19.4 |

Total | - | - | 25.1 | - | 68,614 | 93.9 | 6.4 |

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**MDPI and ACS Style**

Crespo Chacón, M.; Rodríguez Díaz, J.A.; García Morillo, J.; McNabola, A.
Pump-as-Turbine Selection Methodology for Energy Recovery in Irrigation Networks: Minimising the Payback Period. *Water* **2019**, *11*, 149.
https://doi.org/10.3390/w11010149

**AMA Style**

Crespo Chacón M, Rodríguez Díaz JA, García Morillo J, McNabola A.
Pump-as-Turbine Selection Methodology for Energy Recovery in Irrigation Networks: Minimising the Payback Period. *Water*. 2019; 11(1):149.
https://doi.org/10.3390/w11010149

**Chicago/Turabian Style**

Crespo Chacón, Miguel, Juan Antonio Rodríguez Díaz, Jorge García Morillo, and Aonghus McNabola.
2019. "Pump-as-Turbine Selection Methodology for Energy Recovery in Irrigation Networks: Minimising the Payback Period" *Water* 11, no. 1: 149.
https://doi.org/10.3390/w11010149