# Deterministic Model to Estimate the Energy Requirements of Pressurized Water Transport Systems

^{*}

## Abstract

**:**

_{e}(kWh/m

^{3}) is the most popular indicator when characterizing the energy requirements of the water cycle, due to its direct and easy interpretation. In pressurized water transport systems, when referred to an appropriate physical framework (such as a single water transport pipeline), it assesses the efficiency of the process. However, in complex urban water transport networks, I

_{e}only provides a basic notion of the energy needs of the system. The aim of this paper is to define a standard physical framework for assessing the energy intensity in water transport and distribution systems. To that purpose, an analytic expression that estimates I

_{e}is proposed, based on system data and its operating conditions. The results allow for a realistic approximation of the energy needs of water transport. This energy assessment is completed with two context indicators: energy origin (C

_{1}) and topographic energy (θ

_{t}), both essential when the energy efficiency of different systems is to be compared.

## 1. Introduction

_{e}, is relevant for this assessment, as it shows the relationship between both resources (kWh/m

^{3}) and is used to energetically characterize the whole water use cycle.

_{e}, has been widely used as the indicator to characterize the energy of the water use cycle from the beginning [5]. This characterization can be made for the whole water use cycle [6], for its different stages [5], on a global scale [7,8,9,10], by country [11,12], by region [5,13,14], or by city [2,15]. There are plenty of published comparisons [4,16], which can sometimes be complex due to the heterogeneity of the data. For this reason, some scholars have requested improvements in data structure and accessibility, especially in the USA [8,17,18,19,20].

^{3}) to be used in such a way that it captures all its driving factors and reflects the energy use in water transport and distribution. Then a deterministic model is established to predict the total demand of energy. Such a model is valuable for systems at the design and operation stages. The establishment of an adequate physical framework and the cause–effect relationship of the physical system allows the energy pros and cons of the different design alternatives or layouts to be assessed. The energy efficiency of two contextual indicators can be established by comparing the actual energy intensity with the target energy intensity (resulting from the optimization of the system).

_{e}allows the efficiency of the whole process or its individual components to be assessed: sedimentation, ultrafiltration, microfiltration, and osmosis [2,27,28]. In order to compare results, context needs to be taken into account in terms of the water source (surface, marine groundwater) and its quality [3,15,29].

_{e}is very sensitive to the salinity of marine water [30]. In wastewater treatment, the final quality of the effluent is a determining factor in the value of I

_{e}[2,31,32]. Finally, concerning the efficiency of water end uses (with a well-defined framework), I

_{e}comparisons may be reasonably conducted [29,33,34]. This is especially true with those concerning specific uses such as dishwashers, showers, etc. [29,33].

_{e}. Although a trivial choice at first sight, it is only trivial in simple systems (a single pipe pumping from borehole to tank). Complex network systems present different options, some of which are not valid.

_{e}(effect).

_{e}. These indicators characterize the contextual factors that may impact the energy intensity, namely, the source of energy (pumped or gravitational) and the topography of the system. These three elements in conjunction can be used to adequately compare the performance of different systems.

^{3}) to be used in such a way that it captures all its driving factors and reflects the energy use in water transport and distribution. Once the indicator is calculated, a deterministic model based on its value is established to predict the total demand. Such a model is valuable for systems at the design and operation stages. For the first ones, it allows the energy pros and cons of the different design alternatives or layouts to be assessed. For the latter, it allows their energy efficiency to be established, which can be calculated by comparing the actual energy intensity with the target energy intensity (resulting from the optimization of the system).

_{e}) calculation framework for water transport and distribution systems is established. In the following section, the driving factors for I

_{e}are reviewed, and some of the most notable statistical regression models (developed to anticipate the energy demands of utilities) are analyzed, including their limitations. The third section presents an expression, based on the energy equation, that allows the energy intensity (and total energy consumption) of a pressurized water transport system to be anticipated, using the total water volume as an input. This expression can be used to predict the minimum energy required, based on desirable (estimated) operating values. This allows actual performance to be compared with the minimum value, and the efficiency of the process and the performance gap to be determined. Additionally, two context indicators are defined to complement this analysis: energy origin (C

_{1}) and topographic energy (θ

_{t}). These two context information indicators are essential to compare the efficiency of different utilities. Finally, in order to clarify and apply all these concepts, the paper includes a real case study.

## 2. Fundamentals and Methods

#### 2.1. Energy Intensity Framework

- Figure 1, shows a real pressurized network for the irrigation of agricultural plots (Cap de Terme, Spain). Each plot is represented as a node in the model. All nodes are included in the system and supplied from a pumping station (Figure 1a). Following an optimization study, it was determined that it was more energetically efficient to divide the irrigation area in three sectors based on node elevation [36]. As a result, three independent pumping stations were set up, resulting in three fully decoupled individual systems (Figure 1b).

_{e}, has to meet two conditions. The first one is to include all the system’s physical factors that influence the value of I

_{e}. The second condition is to be defined within a physical framework. In practice, average energy intensity is calculated as the sum of all energy consumed by pumps divided by the total registered volume. This ratio fails to capture the actual energy required by pumps, as it disregards leaks and commercial losses which would make the denominator larger.

_{e}indicator correspond to pumping in single pipes, with a reference value of 0.4 kWh/m

^{3}for 100 m of elevation [39]. These systems comply with the framework conditions previously established, as they are physical systems without discontinuities or unbalanced energy inputs, regardless of the pumping station’s location. However, in order to expand the application of this indicator to more complex distribution networks, and as explained previously, networks have to be subdivided in systems and consider gravitational energy.

#### 2.2. Factors Influencing a System’s Energy Needs

- Topography, summarized in three elevation figures: the elevation of the network’s lowest node (which sets the reference level), the elevation of the most energy-demanding node (as explained later, in a few cases it is not the same as the highest node), and the source’s elevation;
- The distances traveled by water;
- The natural energy supplied to the system;Factors linked to service conditions;
- The pressure values at the supply sources (usually zero) and at the delivery nodes (dependent on use), where any excess of pressure over the required value leads to energy loss; and
- The water volume injected to the system V
_{t}, the spatial distribution of water delivered to users (with the corresponding elevations), and the total metered volume V_{r};

- Pumping efficiency;
- Leakage; and
- Friction losses.

_{t}) [36].

- Analytically estimated values (top-down): estimated energy intensity (I
_{ee}), including all the supplied energy (natural and pumped), or the estimated pump energy intensity (I_{ee,p}), only considering mechanical or shaft energy; and - Real values (bottom-up), calculated from real operating data: real energy intensity (I
_{er}), including all supplied energy (E_{s}), and the real pump energy intensity (I_{er,p}), which only accounts for shaft energy (E_{p}).

_{er}with I

_{ee}or I

_{er,p}with I

_{ee,p}. In general, the second pair is used more often, as the required data is easier to obtain by utilities.

#### 2.3. Deterministic Model for the Prediction of the Energy Demand of a System

_{ee}and I

_{ee,p}values are obtained analytically (top-down approach). This section describes the deterministic predictive model for single-source systems. This model is later generalized to consider the case of multi-source systems.

_{ee}and I

_{ee,p}need to be referred to the metered water volume (V

_{r}), as this is the volume used by utilities to calculate the real energy intensity (I

_{er}= E

_{s}/V

_{r}and I

_{er,p}= E

_{p}/V

_{r}). V

_{r}is, by definition, lower than the input volume (V

_{t}), and they are both included in Equation (1) through the water efficiency ratio of both volumes (η

_{le}= V

_{r}/V

_{t}). Energy terms are divided into gravitational energy availability (not impacted by the pumping efficiency, η

_{pe}) and shaft energy requirements. In consequence, greater inefficiencies (η

_{le}and η

_{pe}) lead to worse values for I

_{ee}.

- 0.002725, a unit conversion factor (pressure, expressed in m, to kWh/m
^{3}); - z
_{s}_{,}elevation of the supply source; - z
_{l}_{,}lowest elevation node; - z
_{c}, elevation of the node with the highest energy demand, also known as the critical node (it should be noted that z_{c}is not necessarily the same as the highest node, z_{h}, as friction losses also play a role and difference in elevation could be compensated by additional distance from the source); - h
_{fe}, friction losses from the source to the critical node = ${h}_{f\left(s\to p\right)}+{h}_{f\left(p\to c\right)}$; - ${h}_{f\left(s\to p\right)},$ friction losses from the source to the pumping station;
- ${h}_{f\left(p\to c\right)},$ friction losses from the pumping station to the critical node;
- p
_{o}, service pressure; and - γ: specific weight for water (9810 N/m
^{3}).

_{t}) and its relative importance is provided by the topographic energy context indicator θ

_{t}[43]:

_{1}) indicator. This ratio specifies which percentage of the total supplied energy corresponds to natural or gravitational energy (E

_{n}):

_{n}is the natural or gravitational energy, E

_{p}is the pumped energy, and E

_{s}is the total supplied energy, calculated as the sum of the previous two. Should all supplied energy be gravitational, C

_{1}would be equal to 1, and if all the energy were provided by pumps, its value would be 0. Natural energy has traditionally not been taken into account in energy analyses, and for instance EPANET does not consider it in its energy calculations [44]. However, this energy must be considered when comparing the energy efficiency of different utilities.

_{ee,p}) is a relevant indicator, as it is a benchmark for the real energy intensity (I

_{er,p}) traditionally calculated by utilities. These two indicators do not include natural energy. Therefore, I

_{ee,p}is identical to I

_{ee}(Equation (1)) if the contribution of the natural energy is excluded:

_{1}(energy origin):

_{ee}and I

_{ee,p}), both the total energy (${E}_{se})$ and shaft energy $({E}_{pe})$ needed for a registered water volume V

_{r}can be anticipated, based on the estimated working conditions (values of ${\eta}_{pe}$ and ${\eta}_{le}$):

_{r}, to which the energy intensities have been referred. This volume can be easily converted to the total input water volume (V

_{t}) by deleting the term ${\eta}_{le}$ in the denominators of Equations (1), (2), (6) and (7).

_{ee}and I

_{ee,p}. However, the real indicators to which they must be compared (I

_{er}and I

_{er,p}), are usually averaged values referring to extended periods of time (days, months, or even years). Therefore, it does not make sense to consider hourly variations of the estimated indicators, even though the proposed mathematical formulation allows for it. The weighted average should be calculated for the same period of time to allow for comparison with the real indicator. Consequently, average values of time-dependent variables (e.g., tank water levels) extended over the selected period must be considered.

#### 2.4. Generalization of the Model to Other Systems

_{s}= z

_{h}> z

_{c}is met, with two possible cases:

- The difference in elevation between the source and the critical node is lower than the friction losses plus the service pressure:$${z}_{s}-{z}_{c}<{h}_{f\left(s\to c\right)}+\frac{{p}_{o}}{\gamma}$$
- The difference in elevation between the source and the critical node is equal to or greater than the friction losses plus the service pressure:$${z}_{s}-{z}_{c}\ge {h}_{f\left(s\to c\right)}+\frac{{p}_{o}}{\gamma}$$

_{c}> z

_{s}, considered in Equations (2) to (10) are also valid for gravitational systems.

_{c}is higher than any of the supply sources (there are as many z

_{si}as supply sources). However, being part of a system, the elevations of z

_{c}and z

_{l}are unique. Since pumping efficiencies of the pumping stations can be different, an average pumping efficiency ($\overline{{\eta}_{pe}}$) weighted by volume can be used.

_{e}, is

_{1}) context indicator needs to consider that the natural energy contribution from each source is different, resulting in Equation (6) being expressed as

## 3. Application of the Model to a Real Case. Results and Discussion

- Length = 45.1 km;
- Critical node elevation (in this case, it coincides with the highest node) z
_{c}= 120.66 m; - Pump suction head z
_{s}= 84.00 m; - Elevation of the lowest node z
_{l}= 35.64 m; - Distance between the source and the critical node = 4.5 km;
- Minimum service pressure p
_{o}/γ = 20 m; and - ${h}_{f\left(s\to p\right)}=0$ m (pumping station next to tank).

- Input water volume V
_{t}= 15,386 m^{3}/month; - Metered water volume V
_{r}= 8994 m^{3}/month; - Real water efficiency (includes real and apparent losses) η
_{lr}= 0.58; - Energy consumed by the pumping station ${E}_{p}$ = 3902.25 kWh/ month;
- Average pumping efficiency, η
_{pr}= 0.70; and - Friction losses were estimated at 1.4 m/km [45], resulting in an estimated friction h
_{fe}of 6.3 m.

_{ee}and I

_{ee,p}). Then the predictive capacity of the model was checked by comparing the estimated values with the real ones (I

_{er}e I

_{er,p}), obtained through a bottom-up approach.

_{er}and I

_{er,p}is straightforward:

_{n}:

_{ee}= 0.64 kWh/m

^{3}) and real values (I

_{er}= 0.66 kWh/m

^{3}) concludes that the predictive model is quite accurate.

_{pe}= 0.75 (the EPANET reference value [37]) and η

_{le}= 0.80 (the minimum value adopted by the Portuguese regulator for good leakage management [46]). With these target values, the energy intensity achievable in this sector would be

_{ee,p}= 0.29 kWh/m

^{3}) with the real values (I

_{er,p}= 0.43 kWh/m

^{3}), the improvement margin at the pumping station (I

_{er,p}− I

_{ee,p}) would be 0.14 kWh/m

^{3}. These unit energy savings are achievable by improving the water losses and pumping efficiencies.

_{t}, which can be evaluated with the average elevation (weighed) of the network. In this case, it was 67.7 m.

## 4. Conclusions

^{3}for every 100 m of pumped head) are a representative measure of their efficiency. As a result, the statistical regression models that were presented to estimate the energy needs of transport in a utility are quite local in nature and have limited validity.

_{ee}includes all factors that have an impact on the total energy consumption. Additionally, two context indicators are recommended to provide key information when comparisons between utilities are to be made. The first one, C

_{1}, details the origin of the energy (natural or pumped). The second, θ

_{t}, indicates the weight of the topographic energy (structural energy losses). The management of these losses by their reduction (modification of the layout), recovery (installing PATs), or remove (with pressure reduction valves), the three R, is beyond the scope of this work.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Symbols | Meaning of Symbols |

C_{1} | Energy origin context indicator (kW h) |

E_{s} | Supplied (or injected) energy (kW h) |

E_{se} | Estimated supplied energy (kW h) |

E_{n} | Natural or gravitational energy (kW h) |

E_{p} | Shaft (pumping) energy (kW h) |

E_{pe} | Estimated shaft energy (kW h) |

E_{t} | Topographic energy (kW h) |

H_{c} | Piezometric head of the critical node (m) |

H_{e} | Estimated maximum piezometric head of the system (m) |

H_{i} | Piezometric head of a generic node i (m) |

H_{s} | Piezometric head of source (m) |

H_{s,i} | Piezometric head of source i (m) |

${H}_{s,max}$ | Elevation of the highest source of supply |

h_{fe} | Friction losses from the source to the critical node (m) |

${h}_{f\left(s\to i\right)}$ | Friction losses between the source and the generic node i (m) |

${h}_{f\left(s\to c\right)}$ | Friction losses between the source and the critical node (m) |

${h}_{f\left(s,max\to i\right)}$ | Friction losses between the highest source and the generic node i (m) |

I_{e} | Energy intensity (kW h m^{−3}) |

I_{ee} | Estimated energy intensity (kW h m^{−3}) |

I_{ee,p} | Estimated pump energy intensity (kW h m^{−3}) |

I_{er} | Real energy intensity (m km^{−1}) |

I_{er,p} | Real pump energy intensity (m km^{−1}) |

k | Number of supply sources in the system |

p_{o} | Service pressure (N m^{−2}) |

V_{r} | Metered water volume (m^{3}) |

V_{t} | Total input water volume (m^{3}) |

V_{i} | Input volume from source i (m^{3}) |

V_{T} | Total supplied volume (m^{3}) |

$\overline{z}$ | Weighted average elevation of the system (m) |

z_{c} | Elevation of the node with the highest energy demand (m) |

z_{h} | Elevation of the highest node (m) |

z_{i} | Elevation of a generic node i (m) |

z_{s} | Elevation of the supply source (m) |

z_{s,max} | Elevation of the source with a higher piezometric head (m) |

z_{l} | Elevation of the lowest node (m) |

$\overline{{z}_{s}}$ | Weighted average elevation of the supply sources (m) |

γ | Specific weight of water (N m^{−3}) |

η_{le} | Estimated water efficiency |

η_{pe} | Estimated pumping efficiency |

$\overline{{\eta}_{pe}}$ | Average estimated pumping efficiency |

θ_{t} | Topographic energy context indicator |

## References

- Stahel, W.R. Circular economy. Nature
**2016**, 531, 435–438. [Google Scholar] [CrossRef] [PubMed][Green Version] - Carlson, S.W.; Walburger, A. Energy Index Development for Benchmarking Water and Wastewater Utilities; AWWA Research Foundation: Denver, CO, USA, 2007. [Google Scholar]
- Plappally, A.K.; Lienhard, J.H. Energy requirements for water production, treatment, end use, reclamation, and disposal. Renew. Sustain. Energy Rev.
**2012**, 16, 4818–4848. [Google Scholar] [CrossRef] - Wakeel, M.; Chen, B.; Hayat, T.; Alsaedi, A.; Ahmad, A. Energy consumption for water use cycles in different countries: A review. Appl. Energy
**2016**, 178, 868–885. [Google Scholar] [CrossRef] - Klein, G.; Krebs, M.; Hall, V.; O’Brien, T.; Blevins, B. California’s Water–Energy Relationship. Final Staff Report; California Energy Commission: Sacramento, CA, USA, 2015.
- Sowby, R.B. New Techniques to Analyze Energy Use and Inform Sustainable Planning, Design, and Operation of Public Water Systems. Ph.D. Thesis, University of Utah, Salt Lake City, UT, USA, 2018. [Google Scholar]
- Vilanova, M.R.N.; Balestieri, J.A.P. Energy and hydraulic efficiency in conventional water supply systems. Renew. Sustain. Energy Rev.
**2014**, 30, 701–714. [Google Scholar] [CrossRef] - Sowby, R.B.; Burian, S.J.; Chini, C.M.; Stillwell, A.S. Data Challenges and Solutions in Energy-for-Water: Experience from Two Recent Studies. J. Awwa
**2019**, 112, 28–33. [Google Scholar] [CrossRef] - Liu, F.; Ouedraogo, A.; Manghee, S.; Danilenko, A. A Primer on Energy Efficiency for Municipal Water and Wastewater Utilities; Technical Report 001/12; The International Bank for Reconstruction and Development: Washington, DC, USA, 2012. [Google Scholar]
- Lee, M.; Kellerb, A.A.; Chianga, P.C.; Denc, W.; Wangd, H.; Houa, C.H.; Wue, J.; Wange, X.; Yane, J. Water-energy nexus for urban water systems: A comparative review on energy intensity and environmental impacts in relation to global water risks. Appl. Energy
**2017**, 205, 589–601. [Google Scholar] [CrossRef][Green Version] - Sanders, K.T.; Webber, M.E. Evaluating the energy consumed for water use in the United States. Environ. Res. Lett.
**2012**, 7, 1–11. [Google Scholar] [CrossRef] - Hardy, L.; Garrido, A.; Juana, L. Evaluation of Spain’s Water-Energy Nexus. Int. J. Water Resour. Dev.
**2012**, 28, 151–170. [Google Scholar] [CrossRef][Green Version] - California Public Utilities Commission. Water/Energy Cost-Effectiveness Analysis; Navigant Consulting, Inc.: San Francisco, CA, USA, 2015.
- Ferrer, J.; Aguado, D.; Barat, R.; Serralta, J.; Lapuente, E. Huella Energética en el ciclo Integral del Agua en la Comunidad de Madrid; Fundación Canal: Madrid, Spain, 2017. [Google Scholar]
- Arzbaecher, C.; Parmenter, K.; Ehrhard, R.; Murphy, J. Electricity Use and Management in the Municipal Water Supply and Wastewater Industries; Electric Power Research Institute: Palo Alto, CA, USA, 2013. [Google Scholar]
- Voltz, T.; Grischek, T. Energy management in the water sector. Comparative case study of Germany and the United States. Water-Energy Nexus
**2018**, 1, 2–16. [Google Scholar] [CrossRef] - Chini, C.M.; Stillwell, A.S. Where Are All the Data? The Case for a Comprehensive Water and Wastewater Utility Database. J. Water Resour. Plan. Manag.
**2017**, 143, 01816005. [Google Scholar] [CrossRef] - GAO (United States Government Accountability Office). Amount of Energy Needed to Supply, Use, and Treat Water Is Location-Specific and Can Be Reduced by Certain Technologies and Approaches; US Government Accountability Office: Washington, DC, USA, 2011.
- Sowby, R.B.; Burian, S. Survey of Energy Requirements for Public Water Supply in the United States. J. Awwa
**2017**, 109, 320–330. [Google Scholar] [CrossRef] - WW (Water in the West). Water and Energy Nexus: A Literature Review; Stanford University: Stanford, CA, USA, 2013. [Google Scholar]
- Pelli, T.; Hitz, H.U. Energy indicators and savings in water supply. J. Am. Water Work. Assoc.
**2000**, 92, 55–62. [Google Scholar] [CrossRef] - Duarte, P.; Alegre, H.; Covas, D. PI for assessing effectiveness of energy management processes in water supply systems. In Proceedings of the PI09 Conference. Benchmarking Water Services, The Way Forward, Amsterdam, The Netherlands, 12–13 March 2009. [Google Scholar]
- Cabrera, E.; Pardo, M.A.; Cobacho, R.; Cabrera, E., Jr. Energy audit of water networks. J. Water Resour. Plan. Manag.
**2010**, 136, 669–677. [Google Scholar] [CrossRef] - Bolognesi, A.; Bragalli, C.; Lenzi, C.; Artina, S. Energy efficiency optimization in water distribution systems. Procedia Eng.
**2014**, 70, 181–190. [Google Scholar] [CrossRef][Green Version] - Snider, B.; Filion, Y. A streamlined energy efficiency performance indicator for water distribution systems: A case study. Can. J. Civ. Eng.
**2018**, 46, 61–66. [Google Scholar] [CrossRef] - Bylka, J.; Mroz, T. A Review of Energy Assessment Methodology for Water Supply Systems. Energies
**2019**, 12, 4599. [Google Scholar] [CrossRef][Green Version] - Molinos-Senante, M.; Sala-Garrido, R. Evaluation of energy performance of drinking water treatment plants: Use of energy intensity and energy efficiency metrics. Appl. Energy
**2018**, 229, 1095–1102. [Google Scholar] [CrossRef] - Cooley, H.; Wilkinson, R. Implications of Future Water Supply Sources for Energy Demands; Water Reuse Research Foundation: Alexandria, VA, USA, 2012. [Google Scholar]
- Gerbens-Leenes, P.W. Energy for freshwater supply, use and disposal in the Netherlands: A case study of Dutch households. Int. J. Water Resour. Dev.
**2016**, 32, 398–411. [Google Scholar] [CrossRef][Green Version] - Cabrera, E.; Estrela, T.; Lora, J. Desalination in Spain. Past, present and future. Ing. Agua
**2019**, 23, 199–214. [Google Scholar] [CrossRef][Green Version] - Longo, S.; Mirko d’Antoni, B.; Bongards, M.; Chaparro, A.; Cronrath, A.; Fatone, F.; Lema, J.M.; Mauricio-Iglesias, M.; Soares, A.; Hospido, A. Monitoring and diagnosis of energy consumption in wastewater treatment plants. A state of the art and proposals for improvement. Appl. Energy
**2016**, 179, 1251–1268. [Google Scholar] [CrossRef] - Niu, K.; Wu, J.; Qi, L.; Niu, Q. Energy intensity of wastewater treatment plants and influencing factors in China. Sci. Total Environ.
**2019**, 670, 961–970. [Google Scholar] [CrossRef] [PubMed] - Griffiths-Sattenspiel, B.; Wilson, W. The Carbon Footprint of Water; River Network: Portland, OR, USA, 2009. [Google Scholar]
- Siddiqi, A.; Fletcher, S. Energy Intensity of Water End-Uses. Curr. Sustain. Renew. Energy Rep.
**2015**, 2, 25–31. [Google Scholar] [CrossRef] - White, F.M. Fluid Mechanics; McGraw-Hill: New York, NY, USA, 1979; ISBN 10:0070696675. [Google Scholar]
- Cabrera, E.; Gómez, E.; Soriano, J.; del Teso, R. Towards eco-layouts in water distribution systems. J. Water Resour. Plan. Manag.
**2019**, 145, 04018088. [Google Scholar] [CrossRef] - Rossman, L.A. EPANET 2: User’s Manual; U.S. EPA: Cincinnati, OH, USA, 2000.
- Giustolisi, O.; Berardi, L.; Laucelli, D.; Savic, D.; Walski, T.; Brunone, B. Battle of Background Leakage Assessment for Water Networks (BBLAWN) at WDSA Conference 2014. Procedia Eng.
**2014**, 89, 4–12. [Google Scholar] [CrossRef][Green Version] - Cabrera, E.; del Teso, R.; Gómez, E.; Estruch-Juan, E.; Soriano, J. Quick energy assessment of irrigation water transport systems. Biosyst. Eng.
**2019**, 188, 96–105. [Google Scholar] [CrossRef] - Sanjuan-Delmás, D.; Petit-Boix, A.; Gasol, C.M.; Farreny, R.; Villalba, G.; Suárez-Ojeda, M.E.; Gabarrell, X.; Josa, A.; Rieradevall, J. Environmental assessment of drinking water transport and distribution network use phase for small to medium-sized municipalities in Spain. J. Clean. Prod.
**2015**, 87, 573–582. [Google Scholar] [CrossRef][Green Version] - Lam, K.L.; Kenway, S.J.; Lant, P.A. Energy use for water provision in cities. J. Clean. Prod.
**2017**, 143, 699–709. [Google Scholar] [CrossRef][Green Version] - Madani, K.; Khatami, S. Water for Energy: Inconsistent Assessment Standards and Inability to Judge Properly. Curr. Sustain. Renew. Energy Rep.
**2015**, 2, 10–16. [Google Scholar] [CrossRef][Green Version] - Cabrera, E.; Gómez, E.; Cabrera, E.; Soriano, J.; Espert, V. Energy assessment of pressurized water systems. J. Water Resour. Plan. Manag.
**2015**, 141, 04014095. [Google Scholar] [CrossRef] - Gómez, E.; Cabrera, E.; Soriano, J.; Balaguer, M. On the weaknesses and limitations of EPANET as regards energy. Water Sci. Technol. Water Supply
**2015**, 16, 369–377. [Google Scholar] [CrossRef] - Cabrera, E.; Gómez, E.; Cabrera, E., Jr.; Soriano, J. Calculating the economic level of friction in pressurized water systems. Water
**2018**, 9, 763. [Google Scholar] [CrossRef][Green Version] - ERSAR. Guia de Avaliação da Qualidade dos Serviços se Águas E Resíduos Prestados aos Utilizadores. 3.ª Geração do Sistema de Avaliação; ERSAR: Lisboa, Portugal, 2019.
- Fontanella, S.; Fecarotta, E.; Molino, B.; Cozzolino, L.; Della Morte, R. A performance Prediction Model for Pumps as Turbines (PATs). Water
**2020**, 12, 1175. [Google Scholar] [CrossRef][Green Version] - del Teso, R.; Gómez, E.; Estruch, M.E.; Cabrera, E.; Estruch-Juan, E. Topographic Energy Management in Water Distribution Systems. Water Resour. Manag.
**2019**, 33, 4385–4400. [Google Scholar] [CrossRef] - Papa, F.; Rita Cavaleiro de Ferreira, R.; Radul, D. Pumps: Energy Efficiency & Performance Indicators. In Proceedings of the Efficient 2015-PI 2015 Joint Specialist IWA International Conference, Cincinnati, OH, USA, 20–24 April 2015. [Google Scholar]

**Figure 2.**System with more than one external water source and downstream tanks [37].

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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**

Cabrera, E.; del Teso, R.; Gómez, E.; Cabrera, E., Jr.; Estruch-Juan, E.
Deterministic Model to Estimate the Energy Requirements of Pressurized Water Transport Systems. *Water* **2021**, *13*, 345.
https://doi.org/10.3390/w13030345

**AMA Style**

Cabrera E, del Teso R, Gómez E, Cabrera E Jr., Estruch-Juan E.
Deterministic Model to Estimate the Energy Requirements of Pressurized Water Transport Systems. *Water*. 2021; 13(3):345.
https://doi.org/10.3390/w13030345

**Chicago/Turabian Style**

Cabrera, Enrique, Roberto del Teso, Elena Gómez, Enrique Cabrera, Jr., and Elvira Estruch-Juan.
2021. "Deterministic Model to Estimate the Energy Requirements of Pressurized Water Transport Systems" *Water* 13, no. 3: 345.
https://doi.org/10.3390/w13030345