# Improved Assessment of Energy Recovery Potential in Water Supply Systems with High Demand Variation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Enhanced Methodology for Estimating Energy Recovery Potential

#### 2.1. Preliminary Assessment

_{h}= γQH

_{h}∆t

_{h}is the hydraulic power (W), γ is the water specific weigh (N/m

^{3}), H is the available head (m), Q is the flow-rate (m

^{3}/s), E is the produced energy (kWh), η is the equipment total efficiency (%) and ∆t is operating time (h) in the period of analysis.

#### 2.2. Selection of the Turbomachine and Establishment of the Turbine Flow Rate Range

_{BEP}) and Francis turbines between 60–100%, whereas axial fixed-blade turbines and PAT with no frequency variations operate in much smaller ranges [11].

#### 2.3. Estimation of the Best Efficiency Point Flow Rate and Head Values

_{BEP}as a function of Q/Q

_{BEP}, where H and Q are the head and the flow rate, respectively, and H

_{BEP}and Q

_{BEP}are the head and the flow rate at the best efficiency point, respectively.

_{BEP}is computed based on time series of flow rate at the site. An initial value for Q

_{BEP}is given to start the iterative calculation. The ratio H/H

_{BEP}is then calculated using Q/Q

_{BEP}and the dimensionless head-flow curve. The effectively recoverable head is computed by multiplying H/H

_{BEP}by the best efficiency point head. The corresponding recoverable hydraulic power and produced energy are estimated by using Equations (1) and (2). If power-flow curves are available, power can be directly computed without calculating head.

_{BEP}, H

_{BEP}) are calculated, in an iterative way, using a simple optimization procedure available in Microsoft Excel

^{®}(solver function) in order to maximize the total energy recovered in one year.

#### 2.4. Cost-Benefit Analysis

_{t}/(1 + i)

^{t}]

## 3. Case Study Characterization

## 4. Methodology Application to the Case Study

#### 4.1. Preliminary Assessment of Available Hydraulic Power

#### 4.2. Selection of the Turbomachine and Establishment of the Turbine Flow Rate Range

_{BEP}[11]. The lower limit aims to guarantee the maximum global efficiency of the machine, whereas the upper limit aims not to compromise the service life of the machine. While an approximate constant efficiency of 70% can be achieved at the range of 80 to 100% of Q

_{BEP}[11], dangerous unsteady radial forces acting on the components of the PAT can be avoided, as it has been observed in PAT working in full load conditions [19,20].

#### 4.3. Estimation of the Best Efficiency Point Flow Rate and Head Values

_{BEP}= 1.0283 (Q/Q

_{BEP})

^{2}− 0.5468 (Q/Q

_{BEP}) + 0.5314

_{BEP}= 0.2571 (Q/Q

_{BEP})

^{2}− 0.2734 (Q/Q

_{BEP}) + 0.5314

_{BEP}= 0.1143 (Q/Q

_{BEP})

^{2}− 0.1823 (Q/Q

_{BEP}) + 0.5314

_{BEP}, for the operating flow rate, Q/Q

_{BEP}. The recoverable head H is calculated by multiplying H/H

_{BEP}by the best efficiency point head. A constant value of pressure-head equal to the daily average is used for each hour of the day, since this parameter was not measured in an hourly basis. A minimum backpressure of 5 m was considered in the analysis.

_{BEP}, H

_{BEP}) are calculated by an optimization procedure for the three alternatives aiming at the maximization of the total recovered energy. Estimated best efficiency point flow rate (Q

_{BEP}) is 149 L/s if only one PAT is installed, 81 L/s if two PATs run in parallel and 62 L/s if three PATs are installed. The best efficiency point head is 36 m, considering the minimum available pressure-head over the year (41 m) and minimum backpressure of 5 m. As expected, given the high variability of flow rate at the site and the small operating range of the PAT solution, one single unit can only recover a small part of the available flow (Figure 6a). By increasing the number of PATs, the range of turbined flow increases (Figure 6b,c).

#### 4.4. Energy Recovery Potential

#### 4.5. Cost-Benefit Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Lofman, D.; Petersen, M.; Bower, A. Water, Energy and Environment Nexus: The California Experience. Int. J. Water Resour. Dev.
**2002**, 18, 73–85. [Google Scholar] [CrossRef] - Mamade, A.; Loureiro, D.; Alegre, H.; Covas, D. A comprehensive and well tested energy balance for water supply systems. Urban Water J.
**2017**, 14, 853–861. [Google Scholar] [CrossRef] - Williams, A.A.; Smith, N.P.A.; Bird, C.; Howard, M. Pumps as Turbines and Induction Motors as Generators for Energy Recovery in Water Supply Systems. Water Environ. J.
**1998**, 12, 175–178. [Google Scholar] [CrossRef] - Fecarotta, O.; McNabola, A. Optimal Location of Pump as Turbines (PATs) in Water Distribution Networks to Recover Energy and Reduce Leakage. Water Resour. Manag.
**2017**, 31, 5043–5059. [Google Scholar] [CrossRef] - Gallagher, J.; Harris, I.M.; Packwood, A.J.; McNabola, A.; Williams, A.P. A strategic assessment of micro-hydropower in the UK and Irish water industry: Identifying technical and economic constraints. Renew. Energy
**2015**, 81, 808–815. [Google Scholar] [CrossRef] - Ulanicki, B.; Bounds, P.L.M.; Rance, J.P.; Reynolds, L. Open and closed loop pressure control for leakage reduction. Urb. Water
**2000**, 2, 105–114. [Google Scholar] [CrossRef] - McNabola, A.; Coughlan, P.; Williams, A.P. Energy recovery in the water industry: An assessment of the potential of micro-hydropower. Water Environ. J.
**2014**, 28, 294–304. [Google Scholar] [CrossRef] - Su, P.-A.; Karney, B. Micro hydroelectric energy recovery in municipal water systems: A case study for Vancouver. Urb. Water J.
**2015**, 12, 678–690. [Google Scholar] [CrossRef] - Corcoran, L.; McNabola, A.; Coughlan, P. Predicting and quantifying the effect of variations in long-term water demand on micro-hydropower energy recovery in water supply networks. Urb. Water J.
**2016**, 1–9. [Google Scholar] [CrossRef] - Corcoran, L.; Coughlan, P.; McNabola, A. Energy recovery potential using micro hydropower in water supply networks in the UK and Ireland. Water Sci. Technol. Water Supply
**2013**, 13, 552–560. [Google Scholar] [CrossRef] - Jain, S.V.; Patel, R.N. Investigations on pump running in turbine mode: A review of the state-of-the-art. Renew. Sustain. Energy Rev.
**2014**, 30, 841–868. [Google Scholar] [CrossRef] - Jawahar, C.P.; Michael, P.A. A review on turbines for micro hydro power plant. Renew. Sustain. Energy Rev.
**2017**, 72, 882–887. [Google Scholar] [CrossRef] - Carravetta, A.; Derakhshan Houreh, S.; Ramos, H.M. Pumps as Turbines Fundamentals and Applications, 1st ed.; Springer International Publishing: Cham, Switzerland, 2018; ISBN 978-3-319-67506-0. [Google Scholar]
- Carravetta, A.; Del Giudice, G.; Fecarotta, O.; Ramos, M.H. Pump as Turbine (PAT) Design in Water Distribution Network by System Effectiveness. Water
**2013**, 5, 1211. [Google Scholar] [CrossRef] - ESHA. Layman's Guidebook on How to Develop a Small Hydro Site, 2nd ed.; European Small Hydropower Association: Brussels, Belgium, 1998. [Google Scholar]
- Aggidis, G.A.; Luchinskaya, E.; Rothschild, R.; Howard, D.C. The costs of small-scale hydro power production: Impact on the development of existing potential. Renew. Energy
**2010**, 35, 2632–2638. [Google Scholar] [CrossRef] - Ogayar, B.; Vidal, P.G. Cost determination of the electro-mechanical equipment of a small hydro-power plant. Renew. Energy
**2009**, 34, 6–13. [Google Scholar] [CrossRef] - Monteiro, L.; Delgado, J.; Figueiredo, D.; Alves, R.; Póvoa, P.; Covas, D.I.C. Assessment of the potential for energy recovery in water trunk mains. In Proceedings of the 14th Computing and Control for the Water Industry Conference, Amsterdam, The Netherlands, 7–9 November 2016. [Google Scholar]
- Santolaria Morros, C.; Fernández Oro, J.M.; Argüelles Díaz, K.M. Numerical modelling and flow analysis of a centrifugal pump running as a turbine: Unsteady flow structures and its effects on the global performance. Int. J. Numer. Methods Fluids
**2011**, 65, 542–562. [Google Scholar] [CrossRef] - Fernández, J.; Barrio, R.; Blanco, E.; Parrondo, J.; Marcos, A. Experimental and Numerical Investigation of a Centrifugal Pump Working as a Turbine. In Proceedings of the ASME 2009 Fluids Engineering Division Summer Meeting, Vail, CO, USA, 2–6 August 2009; pp. 471–479. [Google Scholar] [CrossRef]
- Derakhshan, S.; Nourbakhsh, A. Experimental study of characteristic curves of centrifugal pumps working as turbines in different specific speeds. Exp. Therm. Fluid Sci.
**2008**, 32, 800–807. [Google Scholar] [CrossRef] - Fontana, N.; Giugni, M.; Portolano, D. Losses Reduction and Energy Production in Water-Distribution Networks. J. Water Resour. Plan. Manag.
**2012**, 138, 237–244. [Google Scholar] [CrossRef]

**Figure 1.**Water transmission system layout, identification of the three identified sites for energy recovery and detail of the location with highest potential.

**Figure 2.**Historical data of (

**a**) flow rate and (

**b**) pressure-head over one year at the identified location for energy recovery (PA).

**Figure 3.**Annual duration curves of (

**a**) the flow rate and (

**b**) the pressure head. (

**c**) Daily average pressure-head vs. flow rate variation.

**Figure 6.**Turbined flow rate vs. the available flow rate at the site for (

**a**) one PAT, (

**b**) two PATs and (

**c**) three PATs installed in parallel.

**Figure 7.**Daily recoverable energy if (

**a**) one PAT; (

**b**) two PAT and (

**c**) three PAT are installed in parallel.

#PAT | Q_{BEP} (*) (L/s) | H_{BEP} (*) (m) | Power per Unit (*) (kW) | Total Installed Power (kW) | Produced Energy (kWh/Year) | Capital Costs (€) | 10-Year NPV (€) | Payback Period (Years) |
---|---|---|---|---|---|---|---|---|

Preliminary assessment | 120 | 40 | 47 | 47 | 257,169 | 91,650 | 117,926 | 4 |

1 | 149 | 36 | 37 | 37 | 113,586 | 72,150 | 20,415 | 8 |

2 | 81 | 36 | 20 | 40 | 151,180 | 78,000 | 21,800 | 8 |

3 | 61 | 36 | 15 | 45 | 183,787 | 87,750 | 15,311 | 9 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Monteiro, L.; Delgado, J.; Covas, D.I.C.
Improved Assessment of Energy Recovery Potential in Water Supply Systems with High Demand Variation. *Water* **2018**, *10*, 773.
https://doi.org/10.3390/w10060773

**AMA Style**

Monteiro L, Delgado J, Covas DIC.
Improved Assessment of Energy Recovery Potential in Water Supply Systems with High Demand Variation. *Water*. 2018; 10(6):773.
https://doi.org/10.3390/w10060773

**Chicago/Turabian Style**

Monteiro, Laura, João Delgado, and Dídia I. C. Covas.
2018. "Improved Assessment of Energy Recovery Potential in Water Supply Systems with High Demand Variation" *Water* 10, no. 6: 773.
https://doi.org/10.3390/w10060773