**E**ff**ect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: a Numerical and Experimental Analysis**

#### **Óscar E. Coronado-Hernández 1,\*, Mohsen Besharat 2, Vicente S. Fuertes-Miquel <sup>3</sup> and Helena M. Ramos <sup>2</sup>**


Received: 2 August 2019; Accepted: 29 August 2019; Published: 31 August 2019

**Abstract:** The filling process in water pipelines produces pressure surges caused by the compression of air pockets. In this sense, air valves should be appropriately designed to expel sufficient air to avoid pipeline failure. Recent studies concerning filling maneuvers have been addressed without considering the behavior of air valves. This work shows a mathematical model developed by the authors which is capable of simulating the main hydraulic and thermodynamic variables during filling operations under the effect of the air valve in a single pipeline, which is based on the mass oscillation equation, the air–water interface, the polytropic equation of the air phase, the air mass equation, and the air valve characterization. The mathematical model is validated in a 7.3-m-long pipeline with a 63-mm nominal diameter. A commercial air valve is positioned in the highest point of the hydraulic installation. Measurements indicate that the mathematical model can be used to simulate this phenomenon by providing good accuracy.

**Keywords:** air valve; air–water interface; filling; flow; pipelines; transient

#### **1. Introduction**

Entrapped air inside a liquid in a pressurized pipeline system the cause of numerous serious problems in conveying systems. Specifically, the problem tends to be significantly more substantial when a transient flow scenario exists in the system. The transient flow condition can appear as a consequence of different causes, namely a water hammer event, emptying or filling of a pipeline, pump shut down or start up, the existence of leaks, rapid valve maneuvers, and cavitation occurrence. The aforementioned transient events have been studied extensively in previous studies using different numerical models [1]. The valve maneuver is a crucial issue in pressurized pipelines, in which operating a valve without enough care, might create irretrievable accidents. Azoury et al. [2] studied the effect of a valve closure on water hammer using the method of characteristics. The water hammer numerical simulation in conjunction with a column separation occurrence, was studied by Himr [3], and Simpson and Wylie [4]. Saemi et al. [5] presented a study on two- and three-dimensional calculations of the water hammer flows using computational fluid dynamics (CFD) models. In addition, different studies present the water control issue [6–8]. Among the water hammer controlling methods, the air vessel protection device is studied widely due to high reliability [9–12]. The pipeline draining or emptying is the cause of some pipe buckling events in the real-world due to the existence of air pockets in the system that expand during the emptying process. Based on the polytropic law, the air pocket expansion leads to a pressure drop in the

air pocket, which is capable of creating a sub-atmospheric pressure situation. The emptying process has been studied previously numerically and experimentally [13–15]. Furthermore, recent works have been developed to understand the behavior of an air pocket and setting operational rules in the emptying process to prevent future accidents. Several works have been published recently on the numerical simulation of the emptying process using one-dimensional (1D) models in case of having air inside a pipe [16,17]. Other works using advanced CFD techniques have been undertaken on the dynamic behavior of an air pocket over drainage and the effect of backflow air entrance [15,18]. During a flow establishment in a partially or fully empty pipeline, which is usually referred to as the filling process, an air compression situation may emerge. The filling process is capable of inducing very huge spikes of pressure that can lead to damage to the pipeline equipment or eventually induce a pipe rupture. Previous studies have focused on different aspects of the filling process under different conditions [19–23]. The thermodynamic behavior of the system plays a significant role in the transient phenomena. They can be categorized into slow and fast transient events. During a slow transient phenomenon, the heat transfer might be important, and generally, they obey the polytropic law [24]. Nevertheless, in a fast transient phenomenon, the heat transfer can be neglected, and for some ranges of the flow condition, the polytropic law is not valid [25]. In this context, the current study endeavors to reveal some aspects of the inconsistent behavior of the air pocket during the filling process. More studies are needed to address the protection devices or methods for all mentioned transient situations. Usually, surge tanks, air vessels, and different operational valves are used in pipeline systems to prevent extraordinary pressure magnitudes. Among them, air valves are widely used due to the simple application and reliability. However, air valves can act unexpectedly in some transient scenarios. The air valves have been studied by different authors to understand the application of an air valve and its effect on the response of the system [26–30]. In a recent study [31], a mathematical model was developed, which was appropriately verified by experimental results to study the various aspects of the emptying and filling processes, including the effect of air valves. The mathematical model revealed that increasing the air valve size will reduce the spike of the pressure head for the filling process condition. But this was challenged widely by real-world problems, an issue that shows the deficiency of current mathematical models in the prediction of the variation of parameters for the filling process. This motivated the authors of this paper to study the effect of the air valve on the filling process more deeply using mathematical models and present the main source of the problem in the formulation. This research explains in detail, the mathematical model, including all hydraulic and thermodynamic formulations in comparison to a previous publication [31] and tackles the experimental and numerical study of the filling process with entrapped air when different air release conditions are provided. This current study provides extensive information about the unusual behavior of an air pocket with different sizes of air releasement. Indeed, plenty of mathematical models exist for the filling process, but in general, the behavior of air valves has not been addressed.

#### **2. Mathematical Model**

This section presents the mathematical model to simulate a filling process with an air valve in a single pipeline. This process should be a controlled operation, where an entrapped air pocket is compressed by an energy source, and an air valve expels an air volume to relieve pressure surges. Figure 1 shows the scheme of a single pipeline, which consists of a pump or a high-pressure air tank, a length of the filling column, an air valve located at the downstream end, a regulating valve located at the upstream end, and a sloped pipe.

#### *2.1. Assumptions*

The mathematical model assumes the uniform movement of the filling water column. The following assumptions are considered:


**Figure 1.** Scheme of a filling process in a single pipeline with an air valve.

#### *2.2. Formulations*

Based on the aforementioned assumptions, the filling process can be modeled using the following formulations:

• The mass oscillation equation [1,28,31]: This equation represents the water movement adequately since in transient flows with trapped air, the compressibility of the air is much higher compared to the water and pipe system:

$$\frac{dv\_f}{dt} = \frac{p\_0^\* - p\_1^\*}{\rho\_w L\_f} + g\frac{\Delta z\_1}{L\_f} - f\frac{v\_f|v\_f|}{2D} - \frac{R\_v g A^2 v\_f|v\_f|}{L\_f},\tag{1}$$

where *vf* = water velocity, *p*<sup>∗</sup> <sup>0</sup> = initial pressure supplied by tank or pump, *p*<sup>∗</sup> <sup>1</sup> = air pocket pressure, *Lf* = length of the filling column, *t* = time, *D* = internal pipe diameter, *Rv* = resistance coefficient of the regulating valve, *f* = friction factor, ρ*<sup>w</sup>* = water density, *g* = gravity acceleration, Δ*z*<sup>1</sup> = difference elevation, and *A* = cross-sectional area. The relation Δ*z*1/*Lf* (named as gravity term) is calculated for single pipelines as sin θ, where θ represents the pipe slope.

• The air–water interface [28,29]: A piston flow model is considered to represent the interface position, which is applicable in inclined piping installations:

$$\frac{d\mathcal{L}\_f}{dt} = v\_{f,\prime} \tag{2}$$

• The polytropic model of the air phase [30]: This formulation shows the evolution of the air pocket pressure over time by relating the compression of an air pocket (*dVa*/*dt*) to the quantity of the expelled air by an air valve (*dma*/*dt*):

$$\frac{dp\_1^\*}{dt} = k \frac{p\_1^\*}{V\_a} \left(\frac{dV\_a}{dt} - \frac{1}{\rho\_a} \frac{dm\_a}{dt}\right) \tag{3}$$

where *k* = polytropic coefficient, *Va* = air pocket volume, ρ*<sup>a</sup>* = air density, and *ma* = air pocket mass.

• The air mass equation [28]:

$$\frac{dm\_d}{dt} = -\rho\_d v\_d A\_{exp} \tag{4}$$

where *Aexp* = cross-sectional area of an air valve for expelling conditions, and *va* = air velocity. Here the air pocket density (ρa) inside of a pipe system is identical to the air density expelled by an air valve and considering *ma* = ρ*aVa*, thus:

$$\frac{dm\_a}{dt} = \frac{d(\rho\_a V\_a)}{dt} = \frac{d\rho\_a}{dt}V\_a + \frac{dV\_a}{dt}\rho\_a = -\rho\_a v\_a A\_{exp} \tag{5}$$

Based on the variables and parameters shown in Figure 2, then:

$$V\_d = A\mathbf{x} = A(L\_l - L\_f)\_\prime \tag{6}$$

where *x* = air pocket size, and *LT* = total length of the pipe.

**Figure 2.** Location of the air valve.

And deriving the Formulation (6), then:

$$\frac{dV\_a}{dt} = -Av\_f.\tag{7}$$

Plugging Formulations (6) and (7) into (5), then:

$$\frac{d\rho\_a}{dt} = \frac{v\_f A \rho\_a - \rho\_a v\_a A\_{\text{exp}}}{A \left(L\_t - L\_f\right)},\tag{8}$$

• The air valve characterization: Subsonic conditions are required to perform an adequate filling process according to recommendations given by the American Water Works Association (AWWA) [32], thus:

$$v\_a = C\_{exp} p\_1^\* \sqrt{\frac{7}{RT} \left[ \left( \frac{p\_{atm}^\*}{p\_1^\*} \right)^{1.4286} - \left( \frac{p\_{atm}^\*}{p\_1^\*} \right)^{1.714} \right]} \tag{9}$$

where *p*∗ *atm* = atmospheric pressure, *Cexp* = outflow discharge coefficient, *R* = air constant, and *T*= air temperature.

#### *2.3. System Equations and Resolution*

A 5 × 5 system of algebraic-differential Equations (1)–(3), (8), and (9) describes the filling operation in single pipelines. The system has five unknown hydraulic and thermodynamic variables: *vf* , *Lf* , *p*<sup>∗</sup> 1, ρ*a*, and *va*. The resolution is conducted using Simulink in MATLAB.

#### *2.4. Initial and Boundary Conditions*

The system is considered initially static at *t* = 0. Therefore, the initial conditions are described by *vf* (0) = 0, *Lf*(0) = *Lf*,0, *p*<sup>∗</sup> <sup>1</sup>(0) = *p*<sup>∗</sup> 1,0, <sup>ρ</sup>*<sup>a</sup>* <sup>=</sup> 1.205 kg/m3, and *va*(0) <sup>=</sup> 0.

#### **3. Numerical Validation**

#### *3.1. Experimental Facility and Instrumentation*

The mathematical model was validated by experimental tests accomplished in the hydraulic lab of the Instituto Superior Técnico located at the University of Lisbon (Lisbon, Portugal). Sudden pressurization of a trapped air pocket in an undulating pipeline when an air valve was located at the highest point of the pipeline has been addressed. Tests were done in a pipeline having a hydro-pneumatic tank (HT) of 1 m3 upstream to produce the required initial pressure (*p*<sup>∗</sup> <sup>0</sup>) for the tests (see Figure 3). For each test, an air pocket was located at the highest point of the pipeline extending towards the upstream branch of the pipeline. An electro-pneumatic ball valve (BV) was used as a means to isolate the pipeline from the high pressure of the HT prior to starting of the test. So, before starting the test, the BV was closed and pressure in the pipeline was set at the atmospheric range. After adjusting the pressure of the HT (using a pressure gauge), the pressure in the pipeline and the air pocket size, the test started by opening the BV. The BV actuation time was 0.20 s leading to sudden pressurization of the downstream pipeline. The pressure data were recorded by a pressure transducer located at Y = 0.8 m and X = 0 m, which had a frequency of data collection of 0.0062 s. The pressure transducer was able to record the absolute pressure up to 25 bar having a maximum pressure measurement error of 0.5% as reported by the manufacturer. This measurement error was negligible compared to the maximum pressure values attained. The pipeline was composed of several polyvinyl chloride (PVC) pipes creating a length of 7.30 m from the HT to the end of the pipeline. The tests were done by changing different parameters, such as the upstream HT pressure and the air pocket size. A commercial air valve S050 (A.R.I. manufacturer) was used in all tests, which had an internal diameter of 3.175 mm (*Aexp* = 7.92 <sup>×</sup> 10−<sup>6</sup> m2) with an outflow discharge coefficient of 0.32. The resistance coefficient of the BV was 2.2 <sup>×</sup> <sup>10</sup><sup>5</sup> ms2/m<sup>6</sup> for a total opening. The analyzed hydraulic installation can be considered as a single pipeline since transient events occur in the sloped pipe branch due to the valve located at X = 3.0 m remained closed during the experiments.

#### **Figure 3.** *Cont*.

**Figure 3.** Schematic of filling process apparatus.

#### *3.2. Experimental Test*

A total of 8 experimental tests were performed to validate the mathematical model proposed by the authors repeating each measurement twice. Initial air pocket sizes (*x*0) between 0.96 m and 1.36 m were defined in the 1.50-m-long sloped branch pipe in combination with initial gauge pressures (*p*0) of 0.2, 0.5, 0.75, and 1.25 bar in the hydro-pneumatic tank (see Table 1).


**Table 1.** Characteristics of tests.

<sup>1</sup> Absolute pressure in the hydro-pneumatic tank (*p*<sup>∗</sup> <sup>0</sup>) were computed as *p*<sup>0</sup> + *p*<sup>∗</sup> *atm*.

#### *3.3. Model Verification*

To verify the proposed model, comparisons between computed and measured air pocket pressure oscillations were conducted using a constant friction factor of 0.018, considering the previous work published by the authors [16]. The water column located from X = 0 m to X = 3.4 m (see Figure 3) represents a boundary condition of the system since according to the observations it remains static during all measurements; then, it was neglected for the analysis in the mathematical model. The initial length of the water column was always located at the sloped pipe branch (between X= −1.3 m and X= 0 m). Based on these considerations, the hydraulic installation can be modeled as a single pipeline. For the analyses, the proposed model was developed to simulate the filling process until the closure of the air valve, when a single-phase flow (only water) was reached.

Comparisons show that the mathematical model exhibited a good agreement in following the behavior of the air pocket pressure patterns for the first oscillation compared to the measurements, as shown in Figure 4. However, the mathematical model could not simulate the sub-sequence oscillations because the impact of the water column (from X = −3.2 m to X = 0 m) with the blocking water column (from X = 0 m to 3.4 m) is a complex phenomenon where the air–water interface is not perpendicular to the main direction of the pipe installation.

**Figure 4.** Air pocket pressure patterns: (**a**) Test No. 1; (**b**) Test No. 2; (**c**) Test No. 3; (**d**) Test No. 4; (**e**) Test No. 5; (**f**) Test No. 6; (**g**) Test No. 7; (**h**) Test No. 8.

The more important parameter is the hydro-pneumatic tank pressure since its variation implies important differences of values of air pocket pressures. The greater the hydro-pneumatic tank pressure (*p*∗ <sup>0</sup>), the higher the air pocket pressure patterns obtained. With a hydro-pneumatic tank pressure of 0.2 bar (Tests No. 1 and No. 2) a maximum value of air pocket pressure head of 15.0 m was reached; in contrast, using a hydro-pneumatic tank pressure of 1.25 bar, peak values of absolute pressure head of 46.9 m and 44.9 m for Test No. 7 and No. 8, respectively, were reached. Peak values of the air pocket pressure were reached at peak time (*tpeak*). The greater the hydro-pneumatic tank pressure, the lower values of *tpeak* obtained, indicating that a faster compression of the entrapped air pocket was attained. For a hydro-pneumatic tank pressure of 0.5 bar, values of *tpeak* of 0.50 s and 0.52 s for Tests No. 3 and No. 4 were attained, respectively; while for a hydro-pneumatic tank pressure of 0.75 bar, values of *tpeak* of 0.46 s and 0.49 s for Test No. 5 and No. 6 were reached, respectively. The greater the air pocket size (*x0*), the higher values of *tpeak* reached.

On the other hand, the polytropic equation is explained with Tests No. 7 and No. 8 (using an HT of 1.25 bar), where air pocket sizes of 0.96 and 1.36 m generated air pocket pressure heads of 46.9 and 44.9 m, respectively. The smaller the air pocket size, the greater peak of pressure surges attained. The remaining tests do not show representative differences on the reached maximum air pocket pressure because the initial hydro-pneumatic tank pressures were not so high as to appreciate these differences. For instance, a peak value of air pocket pressure head of 21.4 m was reached for Tests No. 3 and No. 4 with initial air pocket sizes of *x*<sup>0</sup> = 0.96 m and *x*0= 1.36 m, respectively. Both the experiment and the mathematical model present these trends.

A summary of experimental results is presented in Table 2, which shows a comparison between maximum values of air pocket pressure head, air pocket size, and attained tpeak.


**Table 2.** Summary of experimental results.

The prediction of the mathematical model can be observed in Figure 5. It demonstrates how the mathematical model developed by the authors has a good agreement with the computation of the maximum air pocket pressure when it is compared with measured values. Hence, the mathematical model can be used to compute the maximum values of air pocket pressure during a filling operation in water installation. It is important to note that the mathematical model properly reproduces the first oscillation and the maximum absolute pressure, but it is not valid for the rest of the hydraulic event.

The selection of a pipe class should consider not only pressure surges occurrence caused by a pump's stoppages or rapid closure of valves but also the peak value reached by the compression of an air pocket during a filling operation.

**Figure 5.** Comparison between calculated and measured maximum air pocket pressure.

#### *3.4. Comparisons Without Air Valve*

To note the action of the air valve S050 on the behavior of the air pocket pressure patterns and how this device can relieve pressure surges occurrence, a comparison of results between using the air valve S050 and neglecting it was conducted in the experimental facility. Figure 6 shows the comparison for Test No. 5, where the air pocket pressure pattern exhibited a similar trend for these two scenarios. The mathematical model presented a better behavior in the prediction of absolute pressure oscillations when there was no air valve compared to the scenario using the air valve S050. The prediction of peak values of air pocket pressure head for both scenarios was detected by the mathematical model, where a maximum value of 32.2 m (at 0.44 s) was reached without air valve, and using the air valve S050 the peak value was 29.3 m (at 0.46 s).

**Figure 6.** Effect of air pocket pressure pattern considering and neglecting the air valve S050 for Test No. 5.

The air valve S050 is used in hydraulic installations to release air bubbles when pipelines are completely occupied by water under a normal situation of operation. The air valve S050 can be used during filling processes, which can reduce low percentages of the maximum air pocket pressure since its small outlet orifice is 3.175 mm, as mentioned by the manufacturer A.R.I. Figure 7 and Table 3 present the peak values of the air pocket pressure head reached. Results show how the air valve can relieve pressure surges from 5% to 9% compared to the scenario when there was no installed air valve.

**Figure 7.** Peak reduction percentage vs. maximum air pocket pressure attained.


**Table 3.** Summary of extreme values of reached pressure surges.

#### **4. Conclusions**

Filling maneuvers in water pipelines generate pressure surges since air pockets are being compressed. The analysis of filling processes without air valves has been studied in detail in recent years; however, there are few studies related to the effects of air valves on the upsurge control, which need a better understanding to reduce pipeline failures during these processes. Air valves need to be positioned along hydraulic installations to expel enough volume of air to relieve peak values induced by air pocket compression.

This research presented a 1D mathematical model to simulate the hydraulic behavior of a water column and the thermodynamic evolution of an air pocket during a filling operation using a commercial air valve. The mathematical model was validated in an experimental facility composed by a 7.3-m-long PVC pipeline with an internal diameter of 63 mm. Air pocket pressure patterns were measured for eight different tests. Comparisons of the air pocket pressure between computed and measured values indicated how the mathematical model is suitable to predict the behavior of the first oscillation, which is very important considering the extreme values of absolute pressure are attained in this period. However, the mathematical model is not valid for the rest of the transient response since the impact between the water column and the blocking water column produces a complex phenomenon, where the air–water interaction is not perpendicular to the main direction of the water pipeline.

The air valve S050 relieves the peaks of air pocket pressure in a ratio ranging from 5% to 9% in the laboratory pipe scale compared to the scenario when this device was not installed. The relief percentages of the maximum air pocket pressure were obtained because the air valve S050 presents a small outlet orifice of 3.175 mm.

The mathematical model can be used to compute the maximum air pocket pressure during filling processes using both undersized and well-sized air valves. However, the analysis of oversized air valves was not covered using the mentioned formulations since more extreme pressure surges can be achieved depending on air pocket size and initial hydro-pneumatic tank pressure.

**Author Contributions:** Conceptualization, Ó.E.C.-H. and V.S.F.-M.; Data curation, Ó.E.C.-H. and M.B.; Methodology, V.S.F.-M.; Writing—original draft, Ó.E.C.-H. and M. B.; Writing—review and editing, H.M.R.

**Funding:** This work is supported by Fundacao para a Ciencia e Tecnologia (FCT), Portugal (grant number PD/BD/114459/2016).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


© 2019 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/).

## *Article* **A New Technical Concept for Water Management and Possible Uses in Future Water Systems**

#### **Pål-Tore Storli 1,\* and T. Sta**ff**an Lundström <sup>2</sup>**


Received: 26 October 2019; Accepted: 28 November 2019; Published: 29 November 2019

**Abstract:** A new degree of freedom in water management is presented here. This is obtained by displacing water, and in this paper is conceptually explained by two methods: using an excavated cavern as a container for compressed air to displace water, and using inflatable balloons. The concepts might have a large impact on a variety of water management applications, ranging from mitigating discharge fluctuation in rivers to flood control, energy storage applications and disease-reduction measures. Currently at a low technological readiness level, the concepts require further research and development, but the authors see no technical challenges related to these concepts. The reader is encouraged to use the ideas within this paper to find new applications and to continue the out-of-the-box thinking initiated by the ideas presented in this paper.

**Keywords:** water management; reservoirs; hydropower plants; pumped storage power plants; hydropeaking; environmental flows

#### **1. Introduction**

Fresh water is a paramount part of any human life and a prerequisite for a developed society and high quality of life. Apart from the obvious use of drinking it, water can provide many services for both society and environments, either in a natural or modified system. The IPCC 2011 climate report (chapter five) has an extensive section (on services and characteristics of Hydro Power Plant (HPP) projects, but transferrable to the general case as well) in which energy and water management services as well as their main environmental and societal characteristics are identified.

For society, these services might be the following: transportation and recreation (riverboats and barges); irrigation; fisheries; energy storage and power production (hydropower production (at HPP)); electric energy storage (Pumped Hydro Storage, (PHS)); waste management; fertilization of farmland (sedimentation by flooding); protection of shorelines (sediments settling in estuaries and river mouths dampening waves and tidal erosion); flood protection (dams and natural lakes reduce flood intensity); and groundwater stabilization.

For environments, the services might be as follows: providing habitat and reproduction areas for living organisms ranging from the smallest protozoa and algae to plants, fish, birds and mammals; the cleaning of river beds during floods; bringing nutrients in the form of sediments to coastal regions; and the settling of sediments to protect ocean shorelines and thus habitats.

The availability of fresh water varies between different parts of the world. Consequently, the use and management of water also vary between countries and continents. Climate changes are predicted to result in changing weather systems, altering the intensity and distribution of precipitation around the globe. The effect of this on the watercourses on a regional and local scale is difficult to predict, as global models must be downscaled into climatic data for use in models of catchments areas [1].

An overall trend seems to be captured in Figure 1, however, which represents the median of 12 climate model projections using the A1B scenario, "A balanced emphasis on all energy sources", from the Special Report on Emissions Scenario by the Intergovernmental Panel on Climate Change (IPCC) [2]. "Climate change has large direct impacts on several aspects of the hydrological cycle—in particular, increases in extremes—making managing and using water resources more challenging" [3].

**Figure 1.** Large-scale changes in annual runoff (water availability, in percent), reprinted from [1].

Current water management systems and infrastructures have been established based on historical data, typically before anthropogenic climate changes were even theorized as being possible. The systems represent large investments and, quite often, incremental additions and/or modifications are not possible, or at least are very expensive. Utilizing the infrastructure to the fullest or even increasing their capacity without modifying the systems is important. When developing the ideas presented in this paper, reusing existing infrastructure has been a guiding principle. The applications presented here are at a low technological readiness level (TRL). As such, cost has not been given any weight in this paper, although it is likely that cost is strongly related to any installation derived from the ideas presented. Hence, a cost–benefit analysis is of course necessary in the long term, but if the benefits are large enough, funding is often available. To put things into perspective, following the 2008 financial crisis, the aid to the financial sector from EU member states was 1400 billion US\$ [4], whereas the worldwide government spending on low-carbon Research and Development (R&D) in 2017 was just above 20 billion US\$ [5]. This means that close to 70 years of global low-carbon R&D funding was used to keep the EU financial system afloat. This strongly indicates that, where there is a governmental and political will, funding is available.

This paper will present novel ideas on how to achieve a new degree of freedom for topics related to water management. This freedom is linked to the active control of the displacement of water by compressed air in different configurations. The objective of this paper is to present the concepts and to get engineers and scientists to "think outside the box", and in this way stimulate ingenuity and the emergence of new technical solutions. The motivation of the authors is stimulate the development of new technical solutions that will provide water management services to society in the future.

The authors acknowledge that part of this paper has the characteristics of a popular scientific publication more than a technical science publication. However, to be able to bring the concepts in focus to a higher TRL, they need to be presented to a technical audience. Furthermore, the actual ways of implementing the concepts might vary depending on the needs of the services required, so a high degree of tailor-made solutions are likely to be needed. This also suggests that presenting something with a high level of technical detail will not aid the objective of this paper, namely to present the concept and induce creativity within the technical community.

#### **2. New Technical Concepts; Method**

The new concepts are based on displacement of water as a method to obtain a new degree of freedom to operate and manage water bodies and flows. Both concepts make use of air as the medium to displace water, but the configurations for obtaining the displacements are different. Problems related to not being able to provide the new degree of freedom are numerous and will be presented in more detail in later sections which will more specifically explain the problems and how displacement can resolve them.

In the next section, the proof for displacement as a method for obtaining a new level of freedom is presented based on first principles. If this proof is not needed from the reader's point of view, this section can be omitted with no loss of continuity.

#### *2.1. Displacing Water Using Compressed Air*

Water is, for all practical purposes, incompressible, meaning that a given mass will have a fixed volume. Decoupling water volume and levels means that a portion of the volume must be moved to a different location. This is called displacement and is what the compressed air is claimed to be able to do in the concepts presented.

Although rather intuitive, in the end, it can be shown mathematically to be true as well. This can be done by utilization of the Reynolds Transport Theorem. This theorem can be applied to any extensive property, such as energy, momentum and mass. It basically describes a control volume (CV) which has inlets and outlets crossing a control surface (CS) and formulates that the rate at which an extensive property *Bsys* is produced/consumed in the system must be equal to the sum of the net flow of *B* through the CS, and the change of the amount of *B* within the CV according to [6]

$$\frac{dB\_{sys}}{dt} = \frac{d}{dt} \int\_{CV} \rho b dV + \int\_{CS} \rho b (\overrightarrow{V}\_r \cdot \overrightarrow{n}) dA\_\prime \tag{1}$$

where ρ (kg/m3) is the density of the fluid carrying the property *B*; *b* = *B*/*m* (*B*/kg) is the intensive property linked to the extensive property; and <sup>→</sup> *Vr* (m/s) and <sup>→</sup> *n* (-) are the relative velocity vector between the fluid and the local CS and the normal vector of the local CS, respectively. Consider two such systems, one for air (subscript a) contained within another one for water (subscript w), as shown in Figure 2:

**Figure 2.** Description of combined air and water systems.

The interphase between the water and air is intended to be flexible—like a balloon—so that it is free to expand or collapse. The quantities . *mw*,*in* and . *mw*,*out* are the mass flow of water in and out of the CV, respectively, while . *ma* is the mass flow of air (positive or negative) through the air inlet.

Two versions of Equation (1) can be constructed, considering that no air or water is produced or consumed ( *DBa Dt* <sup>=</sup> 0; *DBw Dt* = 0); using *B*<sup>1</sup> = *ma*; *b*<sup>1</sup> = *ma*/*ma* = 1; *B*<sup>2</sup> = *mw*; *b*<sup>2</sup> = *mw*/*mw* = 1;

$$\frac{d}{dt} \int\_{\mathcal{C}V, \boldsymbol{w}} \rho\_{\boldsymbol{w}} dV = - \int\_{\mathcal{C}S, \boldsymbol{w}} \rho\_{\boldsymbol{w}} (\overrightarrow{V}\_{r} \cdot \overrightarrow{\boldsymbol{n}}) dA = \dot{m}\_{\boldsymbol{w}, \boldsymbol{\dot{n}}} - \dot{m}\_{\boldsymbol{w}, \boldsymbol{\alpha} \boldsymbol{u} \boldsymbol{\prime}} \tag{2}$$

$$\frac{d}{dt} \int\_{CV,a} \rho\_a dV = -\int\_{CS,a} \rho\_a (\overrightarrow{V}\_r \cdot \overrightarrow{n}) dA = \dot{m}\_a. \tag{3}$$

Assuming the densities to be constant (which holds for low-pressure water, and is a slight simplification for low-pressure air), the densities can be removed in the respective equations, and adding the resulting equations together yields

$$\frac{d}{dt}\left(\int\_{CV,\mu}dV + \int\_{CV,w}dV\right) = Q\_d + Q\_{w,in} - Q\_{w,out\_f} \tag{4}$$

where *Q* is the volume flow (or discharge) of water or air, corresponding to the mass flows. The left-hand side of Equation (4) describes the rate of change of the combined volume of air and water. The right-hand side considers the sum of the discharge through the inlets and outlets. Imagine that a volume of air is submerged in a balloon in a water reservoir (as shown in Figure 2) and for some reason the water level in the reservoir is not allowed to change. This means that the combined volume should be constant, and Equation (4) is simplified to

$$Q\_a = Q\_{w,out} - Q\_{w,in} \tag{5}$$

If no air volume exists, as is the case for existing reservoirs, Equation (5) reduces to *Qw*,*out* = *Qw*,*in*, meaning that the discharge of water into and out of the reservoir must be identical. Thus, Equation (5) show that the presence of the air displacement makes it possible to decouple the water out of and into the reservoir, obtaining the new degree of freedom.

#### Energy Considerations

Even if a new degree of freedom is obtained, some insight into the energy cost of this is appropriate. Using energy *E* (kJ) as the extensive property under investigation in Equation (1), a starting point for an energy analysis of the system can be defined. After divisions of energy into heat (which will be neglected) and work, and further dividing work into work added to the system by a component and pressure work added by the surroundings on the inlets and outlets [6], we get

$$
\dot{\mathcal{W}}\_{shaft} = \frac{d}{dt} \int\_{CV} \rho \mathbf{c} dV + \int\_{CS} \rho \left(\frac{\mathbf{P}}{\rho} + \mathbf{c}\right) (\overrightarrow{V}\_r \cdot \overrightarrow{n}) dA\_r \tag{6}
$$

where . *Wsha f t* (kJ/s) is the power added or extracted by the component(s); *<sup>e</sup>* <sup>=</sup> *<sup>u</sup>* <sup>+</sup> *<sup>V</sup>*<sup>2</sup> <sup>2</sup> + *gz*, where the right-hand side terms are internal, kinetic and potential specific energies, respectively (kJ/kg). This system can be set-up for the water and air configuration in Figure 2, considering the case where the water level must be maintained at a constant level while providing environmental flow *Qw*,*out* while there is no inflow, *Qw*,*in* = 0. The water system has no component that can add (pump) or extract (turbine) power to or from the flow, so there in no . *Wsha f t*-term in this system. However, for the air system, a term . *Wsha f t*,*<sup>a</sup>* appears to represent the power added to inflate it. The development of the equations can be found in Appendix A, yielding

$$
\dot{W}\_{\text{shaft},a} = \lg(\rho\_w - \rho\_a)(z\_s - z\_{\text{cgs},a})Q\_{w,\text{out},\bullet} \tag{7}
$$

where *zs* is the elevation of the reservoir surface and *zcg*, *a* is the elevation of the centre of gravity (COG) of the air body. Further realising that the density of air is much lower than the water density, the term related to the air system will in practise be negligible; consequently,

$$
\dot{W}\_{\text{shaft},a} = g\rho\_{\text{av}}(z\_s - z\_{\text{Q},a})Q\_{\text{av},\text{out}}.\tag{8}
$$

This is the power needed to provide the necessary displacement of water by the air system. Scrutinizing Equation (8), it is recognized that the term represents the power needed to bring the flow from atmospheric pressure to the pressure at the COG of the air body. Another case can be investigated by setting the discharge *Qw*,*out* to a negative value. This case is one in which the water level must be

kept constant, and there is an inflow (negative outflow), but no outflow. In this case, the term . *Wsha f t*,*<sup>a</sup>* will change sign, indicating power will go in the opposite direction. This means that regeneration of power is possible when the air is released from the system. For a full cycle, we thus only must pay the price of energy losses, because the inflation/deflating process is an energy storage process.

#### *2.2. Examples of Use of the New Capabilities*

There are several examples that can be used to highlight some uses of the new capabilities obtained by this decoupling. First, we assume that the water level at its maximum in a reservoir used for hydropower, for instance. The combined volume cannot be increased, because water would be spilled over the dam or through spillways, and it can be assumed that this must be avoided, perhaps due to safety issues or economical concerns. If the draining of water, . *Vw*,*out*, due to capacity issues is smaller than the inflow of water, . *Vw*,*in*, releasing air from the balloon (having negative . *Va*) will keep the volume constant. The volume of air in the CV will decrease, allowing for the water volume to increase, but keeping the sum of the two fixed. For this to be possible, air must be present in the volume prior to this incident occurring. However, the reservoir levels and weather forecast should give an indication of such an incident occurring, and the draining of water can be kept higher than the inflow while air is added to the volume in the hours before the incident. Alternatively, some air volume could be present as a default safety margin. If such air volume—in this case, in the form of a balloon—does not exist, there is no possibility at all of avoiding water to be spilled, and safety is no longer ensured.

The opposite case is if the water is at the minimum allowed level; for example, near the end of the dry season. If the need for water downstream supplied by the draining of water, . *Vw*,*out*, is larger than the inflow of water, . *Vw*,*in*, this is made possible by adding air to the balloon, having a positive . *Va*. Then, the inflating balloon would displace water volume as the water was drained and the level would be kept constant. If such a balloon did not exist, the needed water could not be supplied because this would cause the level to go below the minimum allowable level. Supplying the needed water can, for instance, be of paramount importance to avoid the stranding of fish, [7]. Keeping the level constant can also be of importance for benthic fauna [8].

Both cases above assume that the combined volume should be constant, but the flexibility provided by the displacement can also be used to increase or reduce the combined volume as well, effectively changing the water levels more than what would be the case for mass balance in and out of the reservoirs. Such applications will be discussed later in the paper.

Obtaining the desired displacement can be done in several ways. In principle, a crane could be used to submerge a solid body with a density higher than the water and thus displace a water volume corresponding to the volume of the body. With no indications of these being the only appropriate ways of achieving displacement, two other configurations are considered in this paper; they use an underground cavern and inflatable balloons, respectively. The reasons for choosing these are the fact that much of the infrastructure and components needed are available from other applications existing today and that a gas—in this case, air—is relatively easy to handle. This will be explained in the sections describing the two configurations.

#### 2.2.1. Inflatable Balloons

Displacing water by inflating balloons anchored to the bottom of the water body is the first configuration discussed in this paper. It can be seen in Figure 3.

The principle is intuitively understood and identical to the example used to prove the concept in the section above. Using compressed air to inflate the balloons will displace water, giving the flexibility to operate with a new degree of freedom. Using balloons, the need arises to have strong foundation for the balloons as they experience large buoyancy forces. Although used for a slightly different purpose (compressed air energy storage at great ocean depths), balloons of the type considered appropriate for this configuration have been made and tested in a laboratory [9].

**Figure 3.** Principal drawing of using inflatable balloons.

#### 2.2.2. Air Cushion Underground Cavern (ACUR)

ACUR is an underground cavern excavated for retaining air near a water surface. It can be seen sketched in Figure 4.

**Figure 4.** Principal drawing of the Air Cushion Underground Cavern (ACUR).

The tunnel allowing water to go in or out of the ACUR element is connected to an adjacent water reservoir. Displacing water in ACUR by admitting compressed air will give an addition to the water volume of the adjacent reservoir; vice versa, expanding air from ACUR will allow for water entering it, removing the same water volume from the adjacent water body. ACUR is simply an additional volume in which water can be stored. However, the flexibility obtained by using air to displace water is what gives the possibility of the manipulation of water levels.

Subject to acceptable ground conditions, making ACUR water and air-tight might be a challenge. ACUR must be as close to the water level of the adjacent water body as possible, and this will make the pressure inside ACUR quite low—not significantly higher that atmospheric pressure. There is a resemblance between ACUR and a high-pressure component present in a hydropower plant, called air cushion surge chambers. They are chambers in the rock hydraulically connected to the penstock of power plants and are used where a surge shaft cannot be installed due to the local geographical conditions. They are partially filled with water and air, and the purpose of the surge chamber is to improve the governing stability and reduce retardation pressures when stopping the flow through the power plant, either for regulation of power or shutting down the power plant. The fact that these installations can provide sufficient air and water-tightness despite high pressures indicates that it should be possible to make ACUR air and water-tight as well.

#### **3. Applications**

There are different applications that can be imagined for these concepts. The balloons clearly need a water volume of some size to work, since they are positioned within the water volume. ACUR provides an additional hidden volume and can be constructed adjacent to small rivers and where no significant volume is present, as well as connected to reservoirs. In addition to flow in regulated

rivers, as presented below, the configurations may be used in cities where flooding is a main issue [10]. Watersheds such as rivers, channels, lakes, pools and ponds may be equipped with balloons as shown in Figure 3 to keep the water surfaces at a proper level. During heavy rains, air is released from the balloons, creating a large volume for the water to fill. Once the weather conditions become stable, air can be pumped into the balloons at a slow speed, letting the water leave the city in a controlled fashion.

#### *3.1. Floods, Droughts and Discharge Fluctuation Manipulations*

As Figure 1 shows, run-off is expected to change significantly for most of the planet in the future. Floods and droughts are thus likely to intensify. Since simulations have shown that the ACUR configuration can be used to both mitigate and mimic floods [11], it has a potential to be implemented for rivers and used to dampen the magnitude of the discharge in flood incidents. Destructive floods are ones that are so big that they rarely occur, named by the amount of years between their statistical appearance. A 50-year flood is thus more severe than a 10-year flood. Furthermore, it is the flood peak that is responsible for the level of destruction. Hence, by allowing some of the discharge to enter ACUR, the peak flood discharges can be reduced, making the flood less dangerous. Such a scenario is illustrated in Figure 5.

**Figure 5.** Flood discharge manipulation by ACUR.

The volume needed to turn a 50-year flood into a 10-year flood is of course dependent on the flood characteristics. The duration of the flood peaks tends to be short, so it is not far-fetched to imagine a feasible volume for ACUR being able to relieve the situation. Furthermore, the periods of a flood incident in which the water retrieves rapidly might also be a concern, because an overly high hydro morphological pressure in river embankments might cause landslides. The water stored at the peak flood event could be stored and released to prevent water levels falling too rapidly, hence reducing the risk of landslides. In rivers with many tributaries, ACUR can be used to shift the time of the occurrence of the peak flow of the individual tributaries so that the flood peaks from the tributaries do not all add to the main river flood peak.

In periods of drought, stored water in ACUR can be used for periods where a river flow is at critical levels. The water in the cavern would be subjected to little evaporation, as it is kept away from solar radiation and winds.

Some natural phenomena are triggered by flood-like discharge events. This is might be migratory events for fish in rivers. As an example, the Atlantic salmon migrate from the river as salmon fry in the springtime snow-melt floods [12]. At the other end of the salmon life cycle, the salmon run up the river at high-discharge periods to easily get to the spawning grounds. Mimicking local flood-like events is, for instance, a perfect method to supply water to channels used to attract fish to fish-ways [13,14]. Active use of ACUR could thus facilitate these natural migrations.

In heavily regulated rivers, natural floods have been reduced and silt and sediments have settled in the gravel, which are used by fish as a substrate for hiding fertilized eggs. This has been found to be the case for white sturgeon in the Kootenai River downstream Libby Dam, where the relative rarity of very high flows due to the regulation by the dam is partially responsible for the lack of successful spawning [15]. Therefore, there might be cases in which a regulated river would benefit from a flood-like discharge event. ACUR could be used to provide this as well, by storing water and releasing it when the natural river flow is high, artificially creating a flood-like peak in the discharge. Simply releasing additional high-value water from the reservoir in such a case can be an alternative but carries a high cost. The water stored in ACUR has already given its energy to the generators of the hydroelectric plant and thus has a lower value. The cost of pushing water out of the cavern and into the river would be the cost of operating the compressors providing the pressurized air. In fact, in electrical sub-systems dominated by intermittent energy sources, energy prices have been negative, due to the cost of shutting down wind turbines. Future systems will be dominated by intermittent energy sources, and it is completely feasible that mitigating floods by running compressors will be a net income incident for power companies in the future.

#### *3.2. Energy Storage and Power Production*

ACUR provides an additional volume for storage of water, and at some locations, this additional volume might be very useful. The world is in dire need of reliable, large-scale and fast electrical energy storage technologies. Currently, the best technology by far to provide this is Pumped Storage Power plants (PSP) in addition to large reservoirs. The PSPs are, however, dependent on having both water available as well as a steep terrain with the possibility to construct a reservoir with high elevation. Such locations are not found everywhere, and the best locations have already been developed. The expansion of the power capacity at existing PHS sites has been performed at several locations. This is simply a matter of adding units between the existing upper and lower reservoir. This increases the power that can be produced, but emptying the upper reservoir will then go faster, since the energy storage capacity has not been increased. At some point, the expansion of power at the PSP might be limited by the rate of water level decrease, because a too high rate might introduce too much sediment into the water, or landslides might occur. Installing and operating ACUR to reduce the rate of water level decrease by displacing water into the main reservoir might provide the possibility to add more power by working around this limitation. A suggested position of ACUR in conjunction to the reservoir can be seen in Figure 6.

**Figure 6.** ACUR connected to a reservoir. HRL: highest reservoir level; LRL: lowest reservoir level.

Installing and operating ACUR thus gives the possibility to install more capacity than otherwise possible. Furthermore, the added volume of ACUR represents a novel way of increasing the energy storage capacity at reservoirs. The conventional way of doing this is not easy, because this will in most cases imply that the height of the dam must be increased, and this is not possible in most cases because the additional forces on the construction void the structural integrity of the existing dam (in Europe, this is still possible at several locations due to the high safety factor used when designing the dams due to the cold war). One project in which the dam height was increased due to energy storage increase considerations is at Vianden PHS [16]; however, this dam is not representative of the majority of dams. ACUR represents the possibility of increasing the energy storage at an existing power plant without the need to replace the existing dam.

The position of ACUR below the lowest reservoir level (LRL) in Figure 6 is intentional, and the interested reader can find reasons for this in a previous paper by one of the authors [17]. In that same paper, the ACUR configuration is theoretically demonstrated, showing that the reduction in the efficiency of a pump–turbine cycle due to losses in the compressed air system is small, and that the relative reduction decreases with the increasing head of the PHS.

Water bodies that are currently off-limits for use as reservoirs for pumped storage power plants due to water level limitations might also be allowed for this kind of operation. Imagine two water bodies close to each other with an elevation difference that makes them suitable for pumped hydro; constructing a pumped hydro plant operating between the two water bodies and water displacement capabilities at both bodies would make it possible to operate the plant without any water level changes to either water body by the opposite operation of the displacement capabilities at the two reservoirs. As water is pumped from the lower body, displacement by air would make the level constant. At the upper water body, air would have to be evacuated to make place for the pumped water. Actually, the air could be a closed cycle as well, in which air from the upper part is moved to the lower part simultaneously as water is pumped, counter-cycled to the water. This can be seen in Figure 6, where inflatable balloons are used. ACUR could also be used, but for both applications, the storage is limited to the volume of ACUR/balloons. This might very well be suited for intra-day and hydraulic short-circuit operation for grid stability issues close to a large concentration of energy consumers. In fact, it could be possible to make existing Run-of-River (ROR) power plants operate in a less ROR-like manner. With little or no power production in the power plant, the water level effect of the inflow of water in the upper reservoir could be compensated for by removing the air from the balloons in this reservoir. The same air could be added to the balloons downstream of the powerplant, displacing water and maintaining the flow to the downstream river sections, as seen in Figure 7. When power is needed, the power plant can be ramped up or brought on-line, producing large amounts of power as the air is cycled back again, mitigating any water level and the discharge fluctuations of the reservoir and river. This would change the merit order of the power plant and provide a much-needed addition to the flexibility of the electrical system, allowing the higher penetration of intermittent renewable energy sources into the system.

**Figure 7.** Schematics of counter-cycled water and air Pumped Hydro Storage (PHS).

For hydropower plants (without pumping capabilities), there might be limitations on their operation due to restrictions on the allowed water level in the reservoirs. This is the case for several Nordic hydropower plants, in which the restrictions are typically linked to the summer water level due to fish migration, recreation, transport, etc. The power production capabilities are thus greatly reduced because the level is linked to the volume, and the production of power reduces the volume and thus reduce the level. In such cases, using compressed air to displace volume would lift or ease the

restriction, and the installed capacity would be available for a duration corresponding to the available maximum volume of air. Interestingly, this volume of air is then also available as a volume for flood damping, as the overflow of water can be avoided as the air is expanded, storing the flood. Flood reduction by hydropower reservoirs has great potential socio-economic value; in Norway, as one example, conservative estimates on some waterways estimate several hundreds of million Euros could be saved by the flood dampening capabilities of such reservoirs [18]. As precipitation is expected to be more intense, the capabilities for flood damping by existing hydropower reservoirs might not be sufficient. Furthermore, the Norwegian Water Resources and Energy Directorate has stated that, in a phase where concessions are being renewed, environmental and recreational concerns will be given more weight and will lead to less flexibility due to stronger water level restrictions. This has made Statkraft—the biggest producer of renewable energy in Europe—raise concerns about the future capability of flood protection in Norway [19].

Another possible use of ACUR is at storage hydropower plants with outlets to rivers. Storage power plants are very important for the balancing of the grid because they have the energy storage and power capacity needed to balance baseload generation, intermittent generation and consumption via market mechanisms. This is typically referred to as "hydropeaking" [20]. However, outlets to rivers are often problematic because the discharge to the river can violently fluctuate according to the hydropeaking of the power plant. This is a serious environmental problem because it significantly alters the natural dynamic characteristics of the river flow, affecting the ecology in a negative and often unacceptable way [21]. There are ways of reducing the effect of hydropeaking, and retention/compensation basins are examples of constructional measures [22]. However, there are limitations concerning the flexibility enabled by such basins as well, and additional measures are likely to increase the flexibility further. Using ACUR as a temporary water storage volume and compressed air as an active measure to control the flow out of ACUR will make it possible to smoothen the discharge transients at large operational changes, starts and stops. The layout of this can be seen in Figure 8.

**Figure 8.** ACUR used to smoothen discharge to river, not to scale.

This application of ACUR is currently being investigated in the EU Horizon 2020 project HydroFlex, and the findings are that ACUR is able to smoothen the discharge well, providing the possibility of much faster ramp up/start up and ramp down/shut down of the power plants within current environmental restrictions. This can be seen in Figures 9 and 10, respectively. These results are obtained from a simulation of the power plant Bratsberg [23], which has two identical units. The "Q setpoint" is the target for the governor, which is implemented to control the compressor providing an active use of the ACUR element and represents current limitations due to environmental restrictions. "Q at discharge" is the discharge into the downstream river that results from the operation of the ACUR element. As can be seen, the start-up and shut-down of the units can be performed much faster than the targeted flow due to the presence of the governed ACUR element. The ACUR technique significantly increasing the flexibility of the units. The analysis corresponds to TRL3 and is regarded as proof of concept by the authors.

**Figure 9.** Smoothening of discharge by ACUR at start-up. Reprinted with permission from [23].

**Figure 10.** Smoothening of discharge by ACUR at shut-down. Reprinted with permission from [23].

#### *3.3. Environmental Operation*

Several of the applications already described might be categorized as being initiated by environmental concerns. However, other operations might give additional environmental benefits. In large hydropower and irrigation reservoirs, water can become stagnant and result in an increase in parasitic diseases [24] and other organisms associated with human illness [25]. In such cases, a grid of balloons could be used (a minimum of two if the overall water level is to be kept constant) to circulate water by inflating some balloons with a volume rate of air and at the same time deflating some balloons with the same rate. In this way, water is set in motion within the reservoir. This would contribute to preventing negative effects from occurring due to stagnant water, simply because it would be less stagnant. Such systems are not limited to rivers and power production and can be of interest for the storage of water in general. As a final remark on this, it is noted that most of the undeveloped hydropower potential is in Africa, South America and Asia [26], in climates where there are challenges associated with these kinds of problems.

#### **4. Discussion**

The authors recognize that the concepts described in this paper are far from being deployed, and much research and development is needed before the concepts reach a TRL which make it ready for field-testing. However, the authors see no major technological challenges related to these concepts. Compressors exist today that move large volumes of air against low pressures. The compression heat and subsequent energy loss is not very high for low pressures, if energy recovery from the compressed air is necessary. Constructing caverns and trapping air is understood and has been successfully applied, even at high pressures. Balloons have been made which are intended to be inflated/deflated by air, even at high pressures. Anchoring balloons to the bottom of a reservoir should be a matter of dimensioning.

#### **5. Conclusions**

Climate change is expected to make the task of future water management more difficult. The presented concepts represent a new degree of freedom, which might facilitate this task and

make better use of existing infrastructure. The high degree of conceptuality presented in this paper, along with no indication of cost, makes conclusions on an applicable level difficult. However, the intention of the paper is to stimulate out-of-the-box thinking and the assessment of possible applications among engineers and researchers throughout the community. No technical challenges have been identified that makes the concepts unfeasible, but further research and development must be performed.

**Author Contributions:** Conceptualization, methodology, visualization and writing—original draft: P.-T.S.; funding, acquisition and project administration: T.S.L.; investigation, supervision and writing—review and editing: P.-T.S. and T.S.L.

**Funding:** Parts of this research is funded by European Union Horizon 2020 project HydroFlex grant agreement No 764011, namely the part on using ACUR to smoothen discharge transients from hydropower plants with outlet to rivers.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Appendix A**

Referring to Figure A1, the equations leading to the power needed (Equation (7)) for the operation of the air system are developed here.

**Figure A1.** Schematics of the system.

Adding the two versions of Equation (6) for the systems together, we get

$$
\begin{split}
\dot{W}\_{\text{shaft},\text{\textquotedblleft}\mu} = \frac{d}{dt} \int\_{\text{CV},w} \rho \varepsilon dV + \int\_{\text{CS},w} \rho \left(\frac{p}{\rho} + \varepsilon\right) (\overrightarrow{V}\_{r} \cdot \overrightarrow{n}) dA + \frac{d}{dt} \int\_{\text{CV},\mu} \rho \varepsilon dV \\ \quad + \int\_{\text{CS},\mu} \rho \left(\frac{p}{\rho} + \varepsilon\right) (\overrightarrow{V}\_{r} \cdot \overrightarrow{n}) dA.
\end{split}
\tag{A1}
$$

Replacing the specific energy *e* with the specific energy terms it contains results in

$$\begin{array}{l} \dot{W}\_{\text{sluft},\text{\textit{\textquotedblleft}}} = \frac{d}{dt} \int\_{\text{CV},w} \rho \left( u + \frac{V^{2}}{2} + \mathcal{gz} \right) dV + \int\_{\text{CS},\text{in}} \rho \left( \frac{p}{\rho} + u + \frac{V^{2}}{2} + \mathcal{gz} \right) (\overrightarrow{V}\_{r} \cdot \overrightarrow{n}) dA \\ \qquad + \frac{d}{dt} \int\_{\text{CV},\rho} \rho \left( u + \frac{V^{2}}{2} + \mathcal{gz} \right) dV \\ \qquad + \int\_{\text{CS},\rho} \rho \left( \frac{p}{\rho} + u + \frac{V^{2}}{2} + \mathcal{gz} \right) (\overrightarrow{V}\_{r} \cdot \overrightarrow{n}) dA \end{array} \tag{A2}$$

The further assumptions are as follows: fixed CS for inlets and outlets ( → *Vr* <sup>=</sup> <sup>→</sup> *V*); all integrands are uniform and constant (allowing the integrands to be extracted from the integrals) except for z, for the water volume, which will be addressed later; the air volume expands equally in all directions, making the COG for the air volume constant, thus allowing the z for the air volume to be substituted with the average value *zcg*, *<sup>a</sup>* representing the COG; very small velocities in the volumes making the square of the velocities negligible amount to the following:

$$\begin{array}{l}\dot{W}\_{\text{shaft},\text{a}} = \mu\_{\text{CV},w}\rho\_{\text{w}}\frac{d}{dt}\int\_{\text{CV},w}dV + \rho\_{\text{w}}g\frac{d}{dt}\int\_{\text{CV},w}zdV\\ \qquad + \rho\_{\text{w}}\left(\frac{p\_{\text{w}}}{\rho\_{\text{w}}} + u\_{\text{w}} + \frac{V\_{\text{w}}^{2}}{2} + gz\_{\text{w}}\right)\int\_{\text{CS},w}dQ\\ \qquad + u\_{\text{CV},\mu}\rho\_{\text{aw}}\frac{d}{dt}\int\_{\text{CV},\mu}dV + \rho\_{\text{a}}gz\_{\text{c},\mu}\frac{d}{dt}\int\_{\text{CV},\mu}dV\\ \qquad - \rho\_{\text{a}}\left(\frac{p\_{\text{w}}}{\rho\_{\text{a}}} + u\_{\text{a}} + \frac{V\_{\text{w}}^{2}}{2} + gz\_{\text{a}}\right)\int\_{\text{CS},\mu}dQ\end{array} \tag{A3}$$

All integrals of differentials end up of being the discharge of air or water, hence

$$\begin{split} \dot{W}\_{\text{shaft},\text{a}} &= \mathbf{u}\_{\text{CV},\text{w}} \rho\_{\text{w}} (-\mathbf{Q}\_{\text{w},\text{out}}) + \rho\_{\text{w}} \mathbf{g} \frac{d}{dt} \int\_{\text{CV},\text{w}} zdV + \left(\frac{P\_{\text{w}}}{\rho\_{\text{w}}} + \mathbf{u}\_{\text{w}} + \frac{V\_{\text{w}}^{2}}{2} + \mathbf{g} z\_{\text{w}}\right) \rho\_{\text{w}} Q\_{\text{w},\text{out}} \\ &+ \mathbf{u}\_{\text{CV},\text{a}} \rho\_{\text{a}} Q\_{\text{a}} + \rho\_{\text{a}} g z\_{\text{c}\text{\underline{S},\text{CV},\text{a}}} Q\_{\text{a}} - \left(\frac{P\_{\text{a}}}{\rho\_{\text{a}}} + \mathbf{u}\_{\text{d}} + \frac{V\_{\text{c}}^{2}}{2} + g z\_{\text{a}}\right) \rho\_{\text{a}} Q\_{\text{a}} \end{split} \tag{A4}$$

The lack of losses that practically make the inlet/outlet internal energies equal to the internal energies inside the CVs implies that

$$\begin{split} \dot{W}\_{shft;a} = \rho\_w g \frac{d}{dt} \int\_{CV,w} zdV + \left(\frac{p\_w}{\rho\_w} + \frac{V\_w^2}{2} + gz\_w\right) \rho\_w Q\_{w,out} + \rho\_a g z\_{\text{cg},a} Q\_a \\ - \left(\frac{p\_a}{\rho\_a} + \frac{V\_w^2}{2} + gz\_w\right) \rho\_a Q\_a \end{split} \tag{A5}$$

Using the Bernoulli equation [6] from the surface to the inlet and the outlet of air and water, respectively, yields

$$\frac{P\_s}{\rho\_w} + gz\_s = \frac{P\_w}{\rho\_w} + \frac{V\_w^2}{2} + gz\_{w\prime} \tag{A6}$$

$$\frac{P\_s}{\rho\_a} + gz\_s = \frac{P\_a}{\rho\_a} + \frac{V\_a^2}{2} + gz\_a. \tag{A7}$$

Substituting this back into Equation (A5) results in

$$\dot{\mathcal{W}}\_{\text{shaft},a} = \rho\_w g \frac{d}{dt} \int\_{CV,w} zdV + \left(\frac{P\_s}{\rho\_W} + gz\_s\right)\rho\_w Q\_{w,out} + \rho\_a g z\_{c,\mu} Q\_a - \left(\frac{P\_s}{\rho\_a} + gz\_s\right)\rho\_a Q\_a \tag{A8}$$

which may be rewritten into the following expression:

$$\dot{W}\_{\text{shuff},a} = \rho\_{\text{w}} g \frac{d}{dt} \int\_{CV,w} zdV + (P\_s + \rho\_{\text{w}} g \mathbf{z}\_s) Q\_{\text{w},\text{out}} + \rho\_{\text{a}} g \mathbf{z}\_{\text{g},\text{a}} Q\_{\text{a}} - (P\_s + \rho\_{\text{a}} g \mathbf{z}\_s) Q\_{\text{a}}.\tag{A9}$$

Now, the remaining integral will be addressed. This integral accounts for the rate of change of the potential energy of the water body. This energy is typically found by multiplying the mass with the COG elevation, as is done for the air system in this example. However, the emptying and displacement of water, as in this example, will potentially change the COG for the mass, as well as reducing the mass. If the displacement of water is performed above the COG level of the water, the COG will be pushed downwards. If the displacement of water is performed below the COG of the water, the COG is pushed upwards. This will thus change the potential energy of the mass and must be considered. This is done in the following.

Consider now the air volume filled with water. We can then find the potential energy of the reservoir completely filled with water by adding the integrals for the two volumes of water together. Since we know the shape of the reservoir volume, we also know the value of the COG elevation *zcg*,*res* for this volume *Vres*:

$$
\rho\_{\rm w\mathcal{S}} \int\_{CV, \rm w} zdV + \rho\_{\rm w\mathcal{S}} \int\_{CV, \rm w} zdV = \rho\_{\rm w\mathcal{S}} \int\_{CV, \rm res} zdV = \rho\_{\rm w} g \varepsilon\_{\rm g.res} V\_{\rm res.} \tag{A10}
$$

The integral that represents the part of the volume that contains water in our case is of particular interest; thus, rearranging this, we get

$$\int\_{CV,w} zdV = z\_{\text{cg.res}}V\_{\text{res}} - \int\_{CV,a} zdV. \tag{A11}$$

Using our assumption regarding the iso-directional expansion of the air system, we can rewrite and obtain (as already done in from Equation (A3) to Equation (A4))

$$\int\_{CV,w} zdV = z\_{\text{cg,res}}V\_{\text{res}} - z\_{\text{cg,a}} \int\_{CV,a} dV = z\_{\text{cg,res}}V\_{\text{res}} - z\_{\text{cg,a}}V\_A. \tag{A12}$$

We must now multiply with ρ*wg* and differentiate with respect to time to get the correct term to substitute into Equation (A9):

$$
\rho\_w g \frac{d}{dt} \int\_{CV, w} zdV = \rho\_w g \frac{d}{dt} (z\_{\xi\xi, \text{res}} V\_{\text{res}} - z\_{\xi\xi, \text{a}} V\_A) = -\rho\_w g z\_{\xi\xi, \text{a}} \frac{dV\_A}{dt} = -\rho\_w g z\_{\xi\xi, \text{a}} Q\_A. \tag{A13}
$$

Substituting back into Equation (A9), we get

. *Wsha f t*,*<sup>a</sup>* = −ρ*wgzcg*, *aQA* + (*Ps* + ρ*wgzs*)*Qw*,*out* + ρ*agzcg*,*aQa* − (*Ps* + ρ*agzs*)*Qa*, (A14)

which can be arranged to

$$
\dot{\mathcal{W}}\_{\text{shaft},\mathfrak{a}} = (\mathcal{P}\_{\text{s}} + \rho\_{\text{w}}\mathfrak{g}\boldsymbol{z}\_{\text{s}})Q\_{\text{w},\text{out}} + (\rho\_{\text{d}} - \rho\_{\text{w}})\mathfrak{g}\boldsymbol{z}\_{\text{c}\mathfrak{g},\mathfrak{a}}Q\_{\text{A}} - (\mathcal{P}\_{\text{s}} + \rho\_{\text{a}}\mathfrak{g}\boldsymbol{z}\_{\text{s}})Q\_{\text{a}}.\tag{A15}
$$

In our cases, we want the reservoir volume to be constant, so *Qw*,*out* = *Qa*:

$$\dot{\mathcal{W}}\_{shaft,a} = \left(\rho\_w g z\_s + (\rho\_a - \rho\_w) g z\_{\xi \mathfrak{g},a} - \rho\_a g z\_s\right) \mathcal{Q}\_{w\rho\mathfrak{aut}},\tag{A16}$$

which may be rewritten as .

$$
\dot{W}\_{shaft,a} = \mathcal{g}(\rho\_w - \rho\_a)(z\_s - z\_{\text{c},\text{g},a})Q\_{w,out}.\tag{A17}
$$

#### **References**


© 2019 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/).

## *Article* **Smart Water Management towards Future Water Sustainable Networks**

#### **Helena M. Ramos 1,\*, Aonghus McNabola 2, P. Amparo López-Jiménez <sup>3</sup> and Modesto Pérez-Sánchez <sup>3</sup>**


Received: 2 November 2019; Accepted: 19 December 2019; Published: 21 December 2019

**Abstract:** Water management towards smart cities is an issue increasingly appreciated under financial and environmental sustainability focus in any water sector. The main objective of this research is to disclose the technological breakthroughs associated with water and energy use. A methodology is proposed and applied in a case study to analyze the benefits to develop smart water grids, showing the advantages offered by the development of control measures. The case study showed the positive results, particularly savings of 57 GWh and 100 Mm<sup>3</sup> in a period of twelve years when different measures from the common ones were developed for the monitoring and control of water losses in smart water management. These savings contributed to reducing the CO2 emissions to 47,385 t CO2-eq. Finally, in order to evaluate the financial effort and savings obtained in this reference systems (RS) network, the investment required in the monitoring and water losses control in a correlation model case (CMC) was estimated, and, as a consequence, the losses level presented a significant reduction towards sustainable values in the next nine years. Since the pressure control is one of the main issues for the reduction of leakage, an estimation of energy production for Portugal is also presented.

**Keywords:** smart water management; smart water grids; water drinking network; water losses; energy production

#### **1. Introduction**

#### *1.1. Overview of the Water Sector*

The water industry is subject to new challenges regarding the sustainable management of urban water systems. There are many external factors, including impacts of climate change, drought, and population growth in urban centres, which lead to an increase of the responsibility in order to adopt more sustainable management of the water sector [1]. The coverage of the costs, the monitoring of the non-revenue water (NRW) and the knowledge of the customers' demand for the fairness in revenues are some of the main challenges the water management has to solve [2]. Due to the population growth increasing and a concentration of water needs, a consequent requisite of water management is necessary. Under this reality, the use of advanced technologies, as well as the adoption of more robust management models, are necessary to better suit the water demands [3].

Over the past decades, many parts of the world witnessed the growing water demand, the risks of pollution water supply, as well as the severe water stress. The leading and irreplaceable role that water plays in sustainable development has become increasingly recognized; the management of water resources and the provision of services related to water continues to be minor in the scale of public perception and government priorities of several countries [4]. This lack of water resources is currently satisfied by the water transfer between basins, the desalinization, the regeneration of waste water, and the exploration of wells [5]. The implementation of more efficiency, the water and energy nexus, as well as the water loss control by the best pressure management and smart device implementation, would conduct a sustainable water sector.

#### *1.2. Smart Water Management*

Smart water management aims at the exploitation of water, at the regional or city level, on the basis of sustainability and self-sufficiency. This exploitation is carried out through the use of innovative technologies, such as information and control technologies and monitoring [6]. Hence, water management contributes to leakage reduction, water quality assurance, improved customer experience, and operational optimization, amongst other key performance benefits [7,8]. A smart city can be defined as the city in which an investment in human and social capital is performed, by encouraging the use of "Information and Communication Technology" (ICT) as an enabler of sustainable economic growth, providing improvements in the quality of life of consumers, and consequently, allowing better management of water resources and energy [9]. It is important to recognize that the concept of a smart city is not limited only to technological advances, but aims to promote socioeconomic development [10,11]. Through this model, a city can examine its current state and, in turn, identify the areas that require further development in order to meet the necessary conditions for a smart city [12].

The development of smart techniques requires technology use in the water systems as well as its implementations. Smart water systems are used to improve the situation of many networks characterized by degraded infrastructure, irregular supplies, and low levels of customer satisfaction or substantial deviations of the proportional bills to real consumption. A smart water system can lead to more sustainable water services, reducing financial losses, enabling innovative business models to serve the urban and rural population better [13].

Some of the main advantages of smart water management are a better understanding of the water system, detection of leaks, conservation, and monitoring of water quality. The implementation of smart water system technologies enables public services companies to build a complete database for the identification of the areas where water losses or illegal connections occur. The advantages of smart water grids are economic benefits to water and energy conservation, while the efficiency of the system can improve customer service. The wireless data transmission allows the customers to analyze their water consumption towards preserving and reducing the water bill, in some cases above 30% [14]. Some of the main technologies are be listed as follows:

(i) Smart pipe and sensor; a smart pipe is designed as a module unit with a monitoring capacity expandable for future available sensors [15]. With several smart pipes installed in critical sections of a public water system, real-time monitoring automatically detects the flow, the pressure, leaks and water quality, without changing the operating conditions of the hydraulic circuit. Briefly, the smart wireless sensor network is a viable solution for monitoring the state of pressure and loss of water control in the system. The main advantage compared to other methods of water loss control is the continuous monitoring of the network without local operator intervention and with low energy consumption of the wireless sensor, allowing to remain operational for long periods [16].

(ii) Smart water metering; a smart meter is a measuring device that can store and transmit the consumption with a certain frequency. To develop an efficient water management system, it is necessary to install sensors and/or actuators to monitor the water systems [17]. Therefore, while water meters can be read monthly or one reading every two months with the water bill generated from this manual reading, the smart metering can obtain the consumption at long distance and with a high frequency, providing instant access to the information for customers and managing entities. The management of this information requires an advanced metering infrastructure (AMI), and therefore, the water

companies should install this in order to improve hydraulic and energy efficiency, enabling leakage control as well as illegal connections in terms of water volumes [18].

(iii) Geographic Information System (GIS); GIS plays a strong role in smart water management, providing a complete list of the components along the network and their spatial locations. GIS becomes essential for the management of the water systems, allowing the inclusion of the spatial components in an oriented model to improve the planning and management through a clear evolution of spatial constituents in the network. The major advantage of GIS is the simulation of reality based on data systems designed to collect, store, receive, share, manipulate, analyze, and present information that is geographically referenced [19,20].

(iv) Cloud computing and supervisory control and data acquisition (SCADA); it is referred to the use of memory and storage capacities and calculation of computers and servers shared and linked through the internet, by following the code of network computing. Cloud computing is defined as "a new style of computing in which the resources are dynamically scalable and often virtualized being provided as a service over the internet" [21], such as large repositories of virtualized resources, hardware, development platforms, and software, with easy access and dynamically configured to adapt to different workloads in order to optimize their use. In general, the majority of public water services make supervision, control, and data management through a SCADA system [22,23].

(v) Models, tools of optimization, and decision support systems*;* the implementation of a common framework for measuring the performance based on a set of relevant indicators and data applications and interfaces to support the decision of the managing entities allows the interested parties to evaluate, create trust and confidence, and monitor the improvements [24,25]. The knowledge of reliable short-term demand forecasting patterns is crucial to develop approach models and, therefore, positive decisions in real time to be implemented in smart water systems [26]. These models are focused on simulations, such as Epanet [27] or WaterGems [28]. These tools can be supported using optimization techniques. The programming models can use simulated annealing techniques [29], fuzzy linear programming [30], and multi-objective genetic algorithms in real time [31], among others.

The objective of this research is to disclose the technological breakthroughs associated with water use and the innovations according to the monitoring of water and energy losses, proposing a strategy to improve the efficiency of the system in economic and sustainable terms. The methodology is applied to a real case study of water distribution system (named reference system (RS) due to confidential restrictions). In this network, the water company implemented measures for the monitoring of several parameters, including the water loss control associated with smart water management. This case study was compared using a correlation model case (CMC) in order to predict the benefits of similar actions used in the RS in the CMC, which was proposed in this research using a real database.

#### **2. Materials and Methods**

#### *2.1. Brief Description of Case Study*

Currently, there are technological solutions capable of supporting the management of smart water systems with a high level of efficiency, associated with the reduction of water losses and, consequently, operational costs.

On the one hand, RS integrates several subsystems of water sources, pumping stations, and treatment plants. The RS is composed of approximately 1400 km of pipes, with more than 100,000 service connections, 14 reservoirs, and 10 pumping stations, which allows storage of more than 400,000 m3. The network is modelled by GIS in which the maintenance service is developed according to leakage and break occurrence, interrelating with the customer management database. The network is divided into four different zones that depend on topographic levels. These zones are: low level, which supplies between 0 and 30 m; medium level, which is determined between 30 and 60 m; high level, when the altitude varies between 60 and 90 m; and upper level, which supplies the area above 90 m. It is mandatory that RS has to guarantee a consumed volume of 192 Mm3. However, the NRW was not satisfactory, and the volume stabilized around 50 Mm3. This volume shows the high volume of losses in the distribution network. The data collection in different years over time was provided by the water company.

Due to heavy losses in the RS distribution system noticeable during the night period, RS set the ambitious goal of reducing the NRW to sustainable values, with the mark of water losses set at less than 15% by 2009 (Figure 1).

**Figure 1.** More efficient cities in terms of non-revenue water in the 1990s (based on [11]).

In order to reduce the water losses in 12 years for values less than 15%, RS adopted a well-defined strategy that was focused on: (i) segmentation and continuous monitoring of the network; (ii) development of analysis using internal resources; (iii) optimization of the process of active water losses control; (iv) continuous improvement based on the experience and results; (v) definition of what really is primordial in real cost (investments) control. The reduction of NRW was carried out on both leakage and illegal connections, which were detected through intensive monitoring and metering of the water distribution network.

On the other hand, CMC corresponds to a water distribution in another municipality. The system supplies about 152,000 customers. The water distribution system is composed of 6 reservoirs, which correspond to a total storage capacity of 125,450 m3. The network has 760 km in pipes. The distribution network has approximately 64,000 service connections. The supply is almost entirely gravitational, only actively maintaining the pumping station to fill areas of higher level. At the moment, the distribution network of that city is divided into 18 DMA. The company has opted for the partition of the distribution network through the creation of interior sub-DMA, to be possible to carry out more effective monitoring and consumption control. Then, DMAs are subdivided into 31 sub-DMA.

#### *2.2. Parameters Definition in RS*

The volume of water in the RS, whether imported or extracted, is divided into billed water (BW) and NRW and even between controlled and uncontrolled consumption [32]. The billed water is the consumed water that is directly charged to customers. The NRW is the volume that includes the water losses and the consumed volume by the authorized agents (e.g., social services, fire-fighting services). A simplifying schematic of this water balance is shown in Figure 2.

**Figure 2.** Distribution of the water balance in a drinking system.

Water losses reflect a measure of the quality of management and operation of each system and, consequently, of any water company. Figure 2 shows there are two types of water losses: apparent and real. The apparent or economic losses correspond to the illegal consumption, while the real losses correspond to water losses, ruptures or burst pipelines, reservoirs or service connections up to the point where the customer is connected, and water evaporation in reservoirs. The apparent and real loss volume cannot be exactly separated, and therefore, the improvement of their values should be made using recorded readings as well as increasing the monitoring (i.e., water metering) of the water network. Regarding the water losses control, this proposed strategy shows how to reach the economic level of leakage (ELL) [33]. ELL constitutes the objective value of water companies, in an attempt to minimize the overall costs associated with the water loss. This strategy means the search for the maximum investment, which is feasible compared to the cost of lost water.

The analyzed case studies (i.e., RS and CMC) propose the reduction of water losses in the water distribution system in order to improve the NRW. RS had to improve the monitoring and control of water losses. Thus, RS developed key tools for the deployment of a monitoring system, keeping the system in good operation, with respect to quantity and quality. RS considered the following technologies: (i) Geographical Information System (GIS); (ii) Management Information System for Customers (MISC); (iii) Digital Terrain Model (DTM); (iv) District Metering Areas (DMA); and (v) Hydraulic System Model (HSM).

The application of this strategy made it possible to obtain advantages in terms of quantity and quality system efficiency based on the information available regarding the system operation. In addition, it enabled the identification of consumptions of each DMA, abnormal night consumption, and the management and control of pressure in the water distribution network.

The International Water Association (IWA) recommends that a DMA should have between 1000 and 3000 customers, but in urban areas with high population density, a DMA may group together more than 3000 customers, with a maximum limit of 5000 customers [33]. Hence, the case study was subdivided according to the size of DMA into three different categories: small (DMA with less than 1000 customers), medium (between 1000 and 3000 customers), and large (more 3000 customers). These values have been tested and validated. In RS, the distribution network is divided into 150 different DMA*s*.

In order to carry out the collecting, management, and processing of the information of the water supply system, several registration devices and emitters of data, in particular, data-logging equipment and modems, were used. These devices enabled the automatic collecting data of water consumption, pressure variation, and flow or quality probes directly installed on the network. The data collected are transmitted remotely, through such devices to a central database, where they are stored, offering to the managing entity scans and frequent and reliable records, reducing the need for estimations.

The main objective of an optimization network efficiency (ONE) is to support the strategy focusing on the efficiency and the reduction of losses, providing performance indicators of each DMA. Thus, ONE integrates the process of optimization and improvement of the efficiency of a distribution network including: (i) metering and telemetry; (ii) leakage level definition; and (iii) leakage detection and repair. The implementation of flow meters at the entrance and the exit of each DMA, and the methodologies of innovative strategies for the detection and location of leaks were essential for rapid action and consequent reduction of water and energy losses in the system.

#### *2.3. Methodology to Develop CMC*

The investment analysis in monitoring and water loss control is extrapolated to another distribution system (CMC). Figure 3 shows the proposed methodology to develop the analysis.

**Figure 3.** Flowchart of the methodology to apply the correlation model from reference systems (RS) to correlation model case (CMC).

Hence, the correlation model case (CMC) took the following procedure in the developed study:


by the users; investment of the water company to reduce the water losses and to control the NRW. In contrast, the CMC should establish the deadline to reach the aim, as well as the limit of NRW. In the proposed case study, the deadline was 2025, and the objective value for NRW was 10%.

• Estimation of the necessary investment plan until the deadline: defined the consumption results of the water systems (input data) as well as the determination of the indicators and the defined objective for NRW, a correlation model, and the determination of the annual investment is necessary to develop. The investment plan is focused on the water losses control as well as reducing the unbilled water.

Regression analysis involves the identifying of the relationship between a dependent variable and one or more independent variables. A model of the relationship is hypothesized and estimates the parameter values that are used to develop an estimated regression equation. A simple linear regression is defined by equation (1):

$$
\hat{Y} = a + b\_1 X\_1 + \dots + b\_p X\_p \tag{1}
$$

but it differs as to whether the *X* variables are considered random or fixed [34], and *a*, *b*1, ... , *bp* are coefficients of the correlation equation, '*p*' being the number of variables. In this statistical correlation model, random values of the *X* variables are considered. These variables are obtained in the sample, while the number of cases obtained at each level of the *X* variables is random. Hence, another sample from the same population would yield a different set of values of *X* and different probability distributions of *X*. In the (fixed) regression model, the values of *X* and their distributions are assumed to be, in the sample, identical to that in the population. Some experts have argued that the correlation coefficient is meaningless in a regression analysis since it depends, in large part, on the fixed particular values of *X* obtained in the sample and the probability distribution of *X* [34]. While this relationship between *r* and the distribution of *X* in the sample is certainly true, it does not necessarily follow that *R* and *R*<sup>2</sup> are not useful statistics in a regression analysis.

The fixed regression model fits best with experimental research where there are arbitrarily particular values of the *X* variables and particular numbers of cases at each value of each *X*. Hence, the fixed regression model is most often called the analysis of variance model. However, it is true that it is common practice to apply the regression model to data where the *X* variables are clearly not fixed.

When time or frequency is used to get a confidence interval, *i* means the joint distribution of *X* and the *Y* is bivariate (or multivariate) normal. When the distribution is bivariate normal, then it is also true that the marginal distributions of *X* and *Y* are both normal.

In the optimization of a water distribution network through the improvement of the monitoring and control of losses, the investment required in order to be possible to obtain an equivalent level of performance in other water systems needs to be estimated using a correlation model type.

A statistical analysis using the key indicators of the RS results was developed for the CMC in order to determine the annual growth rates of the number of customers and billed water, and the investment in water losses control per reduced volume of NRW and per client. Note that the determination of those parameters per client is essential to correlate different sizes of water companies.

The correlation between the annual investments per client with the decrease of NRW by the client of the following year is analyzed. This analysis would be able to determine a logistical regression for the investment required per client to achieve a certain level of NRW. Hence, it was determined that the parameter's investment in the water losses control per volume of NRW reduced and per client with the average value of annual investment by the reduction of NRW of the following year and per client by the equation (2):

$$\overline{\text{INV}\_{\text{NRW}}} = \frac{\sum\_{i=1}^{n} \frac{\text{INV}\_{i}}{\text{INRV}\_{i+1}}}{n} \tag{2}$$

where INVNRW is the annual investment average on water losses control by a decrease of NRW and by client; INV*<sup>i</sup>* is the investment on the water losses by client in the year *i*; NRW*i*+<sup>1</sup> is the non-revenue water per client of the year *i* + 1.

Finally, when the correlation was developed, the economic and energy savings were determined according to water metering. Furthermore, the reduction of NRW can contribute to improving other sustainability indicators, such as social, environmental, energy, economy, and technical indicators [35]. Regarding the energy indicators, the improvement affects the network energy efficiency (IEE), excess of supplied energy (ISE), energy dissipation (IED), annual consumed energy (IAE), consumed energy per unit volume (IEFW), energy cost per unit volume implemented (IEC), energy efficiency of pumps when the system is a pump system (IEB), among others. Also, other indicators related to the consumed water will be reduced if the NRW is reduced. A significant indicator associated with the environment is CO2-eq since there is a direct relation between the energy (kWh) consumed in the network and the CO2 emissions (between 582 and 877 gCO2/kWh) [36]. Therefore, the reduction of NRW has high significance in the environmental impact of the water distribution cycle.

The proposed methodology can be used in other case studies when the water managers have enough information available (e.g., recorded and stored data, monitoring of the water systems) to analyze and to implement the corrective measures towards a more efficient water system.

#### **3. Results**

The analysis of the RS case study was carried out based on the results considering a suitable time interval as the most relevant for assessing the effects of the implemented measures in the distribution system. The implementation of the monitoring measures and the active water loss control, allowed RS to reduce the losses in the system from 20% in 2004 to less than 10% of the total volume captured in 2014 (Figure 4).

**Figure 4.** Non-revenue water (NRW) and billed water (BW) evolution at RS.

This decrease of NRW over 12 years was mainly due to the control of the losses in the distribution system (low level zone). In contrast, the BW decreased more than 20 Mm<sup>3</sup> in this period in the distribution system due to environmental concern of society, the leakages control, as well as the reduction of the unbilled water. The policy of monitoring and water loss control of RS was focused in particular on the distribution system (low level zone) since the NRW level was too high in comparison to the treatment and transport of water. The considered goal was ambitious, reducing the NRW in the distribution network for sustainable values, setting a goal of water losses less than 9% by 2016. This work positioned RS in the fifth position of the more efficient cities worldwide (Figure 5). The reduction of water losses was 67.85% compared to values of 1990 (Figure 1), which were considered as the best reference for this water company.

**Figure 5.** More efficient Cities at NRW level in 2016 (based on [11]).

Furthermore, RS still had a decrease in operating costs to the supply network. Despite the reduction of these costs, the unit cost of water produced was not sensitive to this variation and remained close to 0.30 €/m3. This is mainly due to fixed costs of the water supply network, the decrease in demand, and an increase of unit costs of external supplies and services (ESF) in these years, in particular, the electricity.

Still, the energy bill, which is the main constituent of the ESF, contradicted the trend of growth in the market, due to the associated gains with the energy optimization enabled by monitoring and water loss control. In 12 years, RS obtained an energy saving of approximately 65 GWh, reducing the energy bill from more than €6.5 million. In addition to the energy reduction, another more direct result and representative of this policy of monitoring and water losses control was the reduction of the levels of NRW in the network, which allowed a saving close to 200 Mm3 (€60 million) in 12 years.

These results demonstrate the improvement of the efficiency of the RS water network, in which €66 million was saved in 12 years. To reach this saving, the investment in monitoring (e.g., smart watering devices, pressure sensors, communication devices), as well as the control of water losses, were necessary. This investment was €20 million in 12 years. This value was around 30% of the total revenue in this period. This reduction of the consumed energy contributed with a theoretical reduction of 47,385 tCO2-eq according to [36]. The development of this strategy enabled to reduce the overall costs in the operation of the network further, offering a saving of about €46 million in 12 years of operation.

The RS data was used to estimate the major socio-economic indicators to determine the investment required to reach a certain NRW level. The annual growth rate of the number of customers was obtained through the average annual growth recorded by RS from 2004 to 2014, using a growth rate of 0.3% for the developed correlation model. In order to determine the BW progression, firstly, a canonical correlation was prepared considering the evolution of the number of customers in the distribution system in an attempt to assess the dependence of billed water with the number of customers. The obtained regression models are shown in Table 1.


**Table 1.** *R*<sup>2</sup> obtained in the different regression models developed.

After the determination of the correlation model indicators (Table 2), it was possible to relate the annual decrease of NRW with the annual investment in the water losses control required in the previous year. This correlation enabled an investment plan and the evolution of the distribution network features for the next nine years.


**Table 2.** Assessment of characteristic parameters in CMC, based on RS.

The total investment required in the CMC, considering the indicators previously determined, was approximately €9.5 million for that period, allowing a reduction of more than 2.6 Mm<sup>3</sup> of NRW in this period. Table 2 shows the main values obtained from the correlation model.

The obtained investment parameter on the water losses control was 3.6 €/m3 per client and year. In CMC, it was even necessary to determine the volume corresponding to the NRW goal level in 2025. From the BW and the NRW level planned, it is possible to determine the volume of NRW and water in the system for the year 2025. It was determined that these variables are independent, making, from the outset, the demand for a multivariate model in terms of the number of customers and BW. The search model has allowed for determining the evolution of the number of customers and the volume of BW at the CMC system.

#### **4. Conclusions**

In the last few years, the water sector has faced significant challenges, in particular, the effort to develop a smart water system in order to improve efficiency and sustainability performance (e.g., social, technical, and environmental). The developed designations, as well as the analyzed case studies, show that the application of this smart technology does not only contribute to the future of smart cities in terms of water but also to energy nexus, through adequate smart water planning and management.

This application will improve the water sustainability and management, as well as the policy of smart cities adequately adapted considering different constrains. The selected techniques and actions depend on the considered threshold, the capital investment, and the availability of techniques and equipment. In addition, these applied strategies must be associated with a worldwide awareness of society to the sustainable planning and management for the best use of available resources. Through the technological innovations, the smart cities will reduce costs, increase the service quality and optimize the operation of the system. The proposed methodology can also be applied to other water networks contributing to improving system efficiency and sustainability by better management of the water resources.

This research analyzed a real water system named RS (due to the confidentiality of data). In this case study, the results achieved show the implementation of measures for the monitoring and water losses control, which allowed accessing a high level of efficiency, especially the reduction of water losses and the consequent reduction of associated costs. The application of these strategies enabled changing the category of the most efficient cities level, varying its worldwide position from 20th to 5th. However, the calculation of the ELL is sensible for network changes, regional legislation, type of consumption, repair costs, ESF, and the macroeconomic situation of each country. Therefore, although these variables change, the payback period of the investment and the development of strategies to reduce the water losses are viable.

Finally, regarding the excellent results obtained in RS, the necessary investment was estimated to achieve the goal of water losses of 10%, by 2025. So, the CMC was developed and applied, presenting initially with a high level of losses of around 21.5%, requiring a total investment of around €9.5 million until 2025. In some regions, the high level of losses and the need of pressure control also allow the development of complementary solutions based on the implementation of micro-hydropower solutions using by-passes to existing PRVs or at inlets or outlets of tanks and reservoirs. This evaluation demonstrates that a significant potential for technically and economically viable micro-hydropower installations exists, which could make valuable contributions to the energy efficiency and CO2 emission gains in the water sector.

**Author Contributions:** The author H.M.R. contributed with the idea and to the revision of the document and supervised the whole research. M.P.-S. contributed to the correlation model and the analysis of case studies. P.A.L.-J. and A.M. were involved in the revision and suggested guides towards the developed analyses. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors wish to thank the project REDAWN (Reducing Energy Dependency in Atlantic Area Water Networks) EAPA\_198/2016 from INTERREG ATLANTIC AREA PROGRAMME 2014-2020, CERIS, EPAL and ERSAR for the data availability. The authors also thank Teresa Zawerthal for collecting data and the MSc thesis based-study developments under the supervision of Helena M. Ramos.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 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/).

## *Article* **Inline Pumped Storage Hydropower towards Smart and Flexible Energy Recovery in Water Networks**

#### **Helena M. Ramos 1, Avin Dadfar 1, Mohsen Besharat 1,\* and Kemi Adeyeye <sup>2</sup>**


Received: 15 June 2020; Accepted: 5 August 2020; Published: 7 August 2020

**Abstract:** Energy and climate change are thoroughly linked since fossil energy generation highly affects the environment, and climate change influences the renewable energy generation capacity. Hence, this study gives a new contribution to the energy generation in water infrastructures by means of an inline pumped-storage hydro (IPSH) solution. The selection of the equipment is the first step towards good results. The energy generation through decentralized micro-hydropower facilities can offer a good solution since they are independent of the hydrologic cycle associated with climate change. The current study presents the methodology and analyses to use water level difference between water tanks or reservoirs in a base pumping system (BPS) to transform it into the concept of a pump-storage hydropower solution. The investigation was developed based on an experimental facility and numerical simulations using WaterGEMS in the optimization of the system operation and for the selection of the characteristic curves, both for the pump and turbine modes. The model simulation of the integrated system was calibrated, and the conceptual IPSH that can be installed was then investigated. The achieved energy for different technical scale systems was estimated using proper dimensional analysis applied to different scaled hydraulic circuits, as well as for hydropower response.

**Keywords:** pumped-storage; micro-hydropower; water networks; dimensional analysis; pumping system

#### **1. Introduction**

The increasing need for energy in current societies is inducing more emissions of carbon dioxide to the atmosphere worsening the climate change issues. For that reason, the use of renewable energies has received serious attention in recent years. Ensuring a clean environment and a sustainable development of renewable energy sources widely and globally are appointed as future targets (in UN 2030 Agenda [1]). Although there are great interests in wind and solar as green energy sources, the hydropower should not be overlooked with huge given proof. Currently, hydropower is considered as one of the most flexible and preferred sources to produce electricity [2] and for renewable integration. Therefore, the idea of power production using water based on its available flow energy can contribute to the reduction in significant environmental impacts [3,4].

The basic principle of hydropower is driving a turbine by using the power of water through two common configurations: with or without reservoirs. In hydropower with a reservoir, the water can be stored and is able to generate a considerable amount of energy depending on its capacity, while in hydropower without a reservoir, it produces less, operating preferentially with a constant flow, such as water trunk mains or transmission lines [5]. For that reason, among the diverse use of water in multipurpose systems, one usage is increasing for generating energy [6,7]. This is a field in which

large potential in the micro-hydropower (MHP) category with a low or medium head is available in different conveyance systems of water networks [8,9].

Many studies already exist in the literature, but still, there is space for further explorations. In that realm, tubular propeller turbines provide a good possibility that has been addressed in the study [10] presenting an experimental work on the characterization of an inline tubular propeller suitable for pressurized systems, such as water supply and distribution networks, reporting an efficiency around 60% for low-head (below 50 m) operations. Another study [11] has presented an investigation about the reduction in the energy consumption in water pipe networks through the use of low-cost MHPs as a means to exploit the excess pressure within these networks to produce stand-alone electricity production for local or rural consumption. In a case study, Samora et al. [12] developed a method being applied to the city of Fribourg in Switzerland and analyzed the benefits associated with a proposed hydropower scheme. The optimization led to more economic installations, and also combinations of one or more series turbines tested in this study, increasing the energy production. Additionally, a new integrated technical solution with economic and system flexibility benefits is introduced through replacing a pressure reduction valve (PRV) by a pump as turbine (PAT) [13]. In that sense, an implementation in a system having a head between 35 and 90 m reported energy generation of 20 to 94 MWh for flow rate varying between 20 and 50 L/s [14]. Choosing PATs instead of conventional turbines is a good practice that reduces the initial costs of the energy system [15,16]. Additionally, the excess energy in water networks can be recovered to optimize the energy efficiency of the systems [17] equipped with a pump station but presenting an excess of available energy in a gravity pipe branch. In order to use this excess of hydraulic available energy, a water turbine can be installed providing good energy results [17]. Very valuable studies exist on energy generation in water distribution networks (WDNs). Pérez-Sánchez et al. [18] tried to study the sustainability of WDNs by adding energy recovery possibility which leads to an added value to those systems. This study investigated different solutions in energy recovery and provided useful recommendations. Another recent study [19] introduced a novel system for WDNs to control the pressure using a hydraulically operated PRV and generate energy using a PAT. Hydropower generation in a small-scale WDN has also been investigated in another study by using PAT [20]. This study tried to characterize the PAT specification installed instead of a PRV by examining different scenarios. The literature review in WDN shows that most of the energy generation studies use PAT either as a single or hybrid solution. In that realm, Carravetta et al. [21] introduce PAT design strategies for WDNs based on a comparison between hydraulic and electrical regulations in a variable operating strategy. This study showed that the hydraulic regulation of the PAT leads to higher flexibility and efficiency. However, the flow rate is continuously changing in WDNs, which implies having a control system to avoid deficiency in the energy generation. In that case, rather than average values, the daily variation of the flow must be considered. Some studies suggest a real time control (RTC) strategy [22]. Creaco et al. recently presented a comprehensive study of different RTC methods in WDNs [23]. In that scope, Puleo et al. [24] studied the PAT application in WDNs by considering the flow variation that was driven by variable head tanks. This study used a global gradient algorithm to more accurately simulate the network parameters proving that the PAT efficiency is dependent on the network supply and pressure conditions. The flow variation subject is also studied by Alberizzi et al. [25] in a WDN in Italy when a PAT speed control strategy was applied to better exploit the flow rate even in high variations. The introduced strategy was applied and it was possible to provide energy recovery values of the order of 30% higher than a no speed variation scenario. The application of MHP solutions has gone even further to irrigation networks with a promising future of their applicability [26–30]. Additionally, novel solutions using the compressibility effect of air have been presented in some studies [9,31–33] that can be combined with pumped-storage hydropower (IPSH) to offer a hybrid pump–hydro solution. Despite the mentioned studies in this field, it is still worth exploring more aspects. Most of the mentioned solutions are completely dependent on a considerable available head to produce energy that mostly occurs through exploiting PATs. In that

sense, this study tried to examine the idea of creating the required head by adding storage tanks to the system.

Hence, the current study introduces an inline pumped-storage hydropower (IPSH) solution based on experimental tests, numerical simulations and parametric analysis. Among several discussed practical solutions, IPSH can add more flexibility to pumping systems by providing higher head difference enabling the reduction in energy consumption through reusing the pumped water in gravity branches. Since it will not ask for major changes and large additional investments, using a by-pass to the main pumping system can offer a profitable hydro-energy solution. Among the energy generated, the water power potential energy is more flexible, adaptive and feasible to combine with other renewable sources to feed the pumping system as a hybrid solution. Based on that, this study aims to (a) define the electromechanical selection rules; (b) present a conceptual idea of energy generation by using storage tanks in WDN; (c) analyze results from an experimental small-scaled system by means of numerical simulations to calculate energy generation in a conceptual energy recovery prototype; (d) use suitable dimensional analysis (for hydraulic system and turbomachinery) to predict energy output in different systems' scales. In general, this study presents a low-cost energy prediction using a pumped-storage hydropower solution through experimental measurements, calibration of the numerical model and dimensional analyses.

#### **2. Electromechanical Equipment**

#### *2.1. Pump Characteristics*

#### 2.1.1. Characteristic Curves and Operational Point

Pump characteristic curves describe the relationship between the flow rate and the pump head for a specific pump type (Figure 1). Other important information is graphs for different impeller diameters, the net positive suction head (NPSH), the efficiency and power curves. In the case of any pump, its designation determines its specific nominal discharge impeller diameter. The pump's efficiency throughout its characteristic curve should not drift too much from the best efficiency point (BEP). The motors whose pole number is associated with the rotational speed value also have their own efficiencies to be considered.

**Figure 1.** Typical pump characteristic curves: head, efficiency, NPSH and power curves.

The operation point in each pump curve is dependent upon the characteristics of the system in which it is operating. The system head curve is the head equation or the relationship between flow and hydraulic losses in the hydraulic system. Figure 2 shows the pump's operating point (*Q*1, *H*1) which can change with the differential water level, closure flow control valve or the rotational speed of the pump.

**Figure 2.** Representation of a single and parallel pump curves.

When two or more pumps were installed in parallel, the increasing of flow rates were obtained (Figure 2). The operating point (*Q*2, *H*2) represented a higher volumetric flow rate than a single pump for a consequence of greater system head loss, and the volumetric flow rate was lower than twice the flow rate achieved by using a single pump (*Q*2,1 < *Q*1). All of these changes can influence the system efficiency.

The affinity laws expressed in Equation (1) represent the mathematical relationship between the rotational speed (*n*), flow rate (*Q*), head (*H*) and pump power (*P*) for the same impeller diameter. The pump specific speed is given by Equation (2).

$$\frac{N\_1}{N\_2} = \frac{Q\_1}{Q\_2} = \sqrt{\frac{H\_1}{H\_2}} = \sqrt[3]{\frac{P\_1}{P\_2}}\tag{1}$$

$$m\_{sp} = N \frac{Q^{1/2}}{H^{3/4}}\tag{2}$$

Variable speed drive (VSD) in pumps induces smooth speed variations of the rotating shaft, directly proportional to the flow, translating into significant pump power variations, which can increase the efficiency of the pumping operation when compared to pumps equipped with fixed speed drive (FSD). Nevertheless, this also affects the pump head, rendering it inoperable below the point where it will not cross the system curve. As possible operating points come closer the operation of the pump becomes unstable if transient regimes occur, inducing the flow variation. Additionally, the pump curve can have a shut-off head inferior to the system curve, meaning that the pump is not able to start at that particular speed.

#### 2.1.2. Selection of a Pump

In a water network system, the total water supply needed by the population must be met by the operation of one or more pumps, whereby the flow rate must be superior to the average daily demand, considering pumps with a flow up to double that value. Regarding the total head, the pumps should comprise a range which takes into account the increase in roughness of the pipes over time such as through Hazen–Williams (H–W) roughness coefficients. Based on the available pump curve, the pump needs to be suitable for its water supply system (WSS) or it will probably operate with reduced efficiency or even with flow instabilities. To have a real idea with a pump efficiency at a BEP of 72% and a motor with 92% efficiency, the total efficiency at that point is 66%. Since the operating

point is far from the BEP, the operational costs resulting from additional energy consumption can be quite significant.

Then, in a pump system design, several pumps which fitted the considered flow and head ranges can be selected, such as the practical application presented in Figure 3.

**Figure 3.** Different pumps and system curves for different head losses.


It is also relevant to analyze the speed range in which a pump can operate, where the solution space in the optimization process by the hydraulic simulator WaterGEMS does not include unfeasible solutions, which is determined by comparison to the system curve. The selection has to avoid system instability considering all the former considerations on the pump selection.

#### *2.2. Pump as Turbine Curves*

When a pump works in the turbine zone, the motor will operate as a generator. During pump operation, the discharge, *Q*, is a function of the rotating speed, n, and the pumping head, *H*, whereas the alteration of the speed will depend upon the torque of the motor, *T*.

For normal turbine operation, the rotating speed (*n*) and discharge (*Q*) were negatives and the head (*H*) and torque (*T*) were positives (Figure 4).

**Figure 4.** Pump operation zone in the third quadrant and characteristic parameters [34].

Based on pumps operating as turbines, the turbine characterization was developed by the following next steps: (i) different parameters must be defined based on an established database of synthetic PATs (a large number of different PATs) through characteristic curves that are shown in Figure 5 as well as changing the specific speed (*nsT*) defined according to Equation (3):

$$m\_{sT} = N\_R \frac{P\_R^{1/2}}{H\_R^{3/4}} (\text{im}m, k\mathcal{W}) \tag{3}$$

where *NR* is the rated rotational speed in rpm, *PR* is the rated power in kW, *HR* is the rated head in m, since *R* means the rated conditions or the PAT design point for the best efficiency condition; (ii) when the specific speed is defined, *nsT* the values of head number (ψ) for each flow rate number (ϕ) can be estimated. When the specific speed was defined and the *ns* was not known, the values of head number (ψint) and efficiency (ηint) for each discharge number value (ϕint) were estimated by linear interpolation. When the non-dimensional number was defined, for each diameter and rotational speed (*N*) the head and efficiency curves were determined by Equations (4)–(6):

$$Q = q \rho\_{\rm int} N D^{\beta} \tag{4}$$

$$H = \frac{\psi\_{\rm int} N^2 D^2}{\mathcal{g}} \tag{5}$$

$$
\eta = \eta\_{\text{int}}(q\_{\text{int}}) \tag{6}
$$

**Figure 5.** Pump as turbine (PAT) characteristic curves for different specific speed values, based on experimental tests and affinity laws (adapted from [25]): (**a**) efficiency curves; (**b**) head curves.

Hence, the correspondent net head and flow rate for the turbine mode will be also influenced by the system curve of the hydraulic system as represented in Figure 5.

#### **3. Methodology**

This research used a hydraulic numerical simulation model of an energy recovery system to evaluate the conceptual idea of an IPSH solution and also to estimate the potential energy available in a WSS. This approach used an experimental apparatus of a pumping system to collect the required data of pressure, flow rate, efficiency and rotational speed of a pump for a certain controlling flow. These data were exploited to establish a numerical model using a WaterGEMS simulation tool and also to calibrate the model for different operating conditions. When the numerical model for the pumping system was validated to reproduce the measured data, it was upgraded by adding a by-pass branch to create the desired energy recovery system. The numerical results from the model were used to estimate the energy output of a possible energy recovery solution. This approach has been depicted in the current section by, first, discussing the experimental system and presenting measurement data. The experimental system is known as the base pumping system (BPS) since it is the base of the future energy recovery system. Then a discussion about the calibration of the numerical model will be provided. This section will be closed by introducing the energy recovery system known as inline pumped-storage hydropower (IPSH) through numerical modelling in a WaterGEMS environment.

#### *3.1. Base Pumping System (BPS) and Experimental Results*

#### 3.1.1. System Configuration

The experimental facility BPS is located at the laboratory of hydraulic (LH), Instituto Superior Técnico, Universidade de Lisboa and consists of several components (Figure 6): (a) a centrifugal pump that feeds the loop pipe system; (b) an interface control panel; (c) an electromagnetic flow meter to measure the instant flow (SC-1); (d) flow control valves along the pipe at the inlet and outlet of the pumps (VR-1 and VR-2); (e) pressure transducers (SP-1 and SP-2) to record the pressures; (f) a free-surface reservoir (water tank). Pipes are made of polyethylene with a diameter of 25 mm and a total length of 198 cm.

**Figure 6.** Experimental facility at Instituto Superior Técnico (IST) lab.

The measuring range of the mentioned sensors is presented in Table 1. A three-phase motor activated the pump, while the interface control panel provided the possibility of adjustment and measurement of the rotating speed and also the transmitted mechanic torque.


**Table 1.** Measuring range of test parameters.

A free surface tank with a capacity of 85 dm3 existed at downstream of the operating system. A valve located at downstream made it possible to induce flow variations by maneuvering and applying local head loss of the valve. An electromagnetic flowmeter (SC-1) and two pressure transducers (SP-1 and SP-2) were used to record the flow rate and pressure data, respectively. Different tests were carried out for different conditions depending on the different opening percentages of the VR-2 valve and also the pump rotational speeds, as presented in Table 2. The data measurements included the flow rate (*Q*), head (*H*), rotational speed (*N*), pump upstream and downstream pressures, the efficiency of the pump (η) and hydraulic and mechanic powers *Ph* and *PM*, respectively).

**Table 2.** Experimental tests specifications.


#### 3.1.2. Experimental Results

During the pump operation, the flow rate was a function of the rotational speed and the pumping head [35]. The flow rate varied from zero, for a fully closed valve, to 61.98 L/min for a rotational speed of 2950 rpm, as shown in Figure 7. Additionally, the minimum and maximum measured heads were 1.8 and 16.92 m for rotational speeds of 1600 and 2950 rpm, respectively. Hence, Figure 7 presents characteristic curves for different rotational speeds, flow rate and head, covering the range of operation for the pumped storage system and efficiency variation for *N* = 2950 rpm.

**Figure 7.** Characteristic curves obtained from the experimental tests.

#### *3.2. Model Calibration*

To perform the system analyses, it was necessary to calibrate the numerical model based on the measured data. The WaterGEMS software from Bentley was used for numerical simulation providing an optimized simulation tool and a user-friendly environment for water distribution networks. WaterGEMS calculated the hydraulic head and pressure at every node along with the flow rate, the flow velocity and the head loss in each pipe branch and as well as the hydraulic head using the gradient algorithm based on the EPANET solver. The water system shown in Figure 8 was built by including one tank, one centrifugal pump and two flow control valves similar to the experimental setup. The experimental setup (shown in Figure 6) is called BPS (base pumping system) in this paper.

**Figure 8.** Scheme of the base pumping system (BPS) in the mathematical model and experimental apparatus.

The calibration process involved the optimization of BPS parameters correspondent to actual measured conditions [35,36]. The BPS was calibrated considering the characteristic curves of the pump, for several pump rotational speeds and valve opening percentages (TCV-2).

Hence, in the simulation process, a variable speed pump (as a VSD) was introduced into WaterGEMS through proper pump curves. The rated pump characteristic curve was defined for the maximum rotational speed, i.e., 2950 rpm, and for each different rotational speed a relative speed factor (RSF) was defined as a coefficient of this maximum rotational speed. A throttle control valve was also defined to induce different flow rates into the system by the partial opening of the valve. In summary, each test was simulated by defining proper RSF and then changing opening flow percentages as in Table 2. This process was repeated for different RSFs until all the rotational speeds were simulated. During this simulation process, the valve discharge coefficients and other associated losses were optimized and calibrated. Results obtained from the simulation by WaterGEMS presented in Figure 9a show good relative accordance with the measured data, associated with scale effects, offering the root mean square errors (RMSEs) shown in Figure 9b with an average of around 0.72. The numerical model calibration based on experimental data guaranteed reliability to follow simulations that take place to assess the behavior of a new adaptation system for energy recovery.

**Figure 9.** Comparison of experimental and numerical results for the BPS; (**a**) head and flow rate; (**b**) root mean square error (RMSE).

A traditional pumping system is composed of different elements that correspond to energy consumption and head losses. However, interesting potential usually exists in pipe branches of pumping systems for energy recovery which can supply energy to treatment plants, electric data base measurement and control devices, and in general, reduce costs of energy in water networks.

#### *3.3. Pumping System Operation*

The best efficiency point (*QR*, *HR*, η*R*) of the pump was characterized by a flow rate of 35 L/min, with a head of 13.5 m and an efficiency of 75% for the rotational speed of 2950 rpm and specific speed 10.05 (Table 3).



The characteristic curves in the dimensionless form (Figure 10) were constructed based on a rated condition associated with the best efficiency point. The dimensionless curves provided a tool to transfer information to other equivalent systems.

**Figure 10.** Dimensionless pump characteristic curves for different rotational speeds.

The best efficiency point of the pump was selected to present the head and efficiency variations with a flow rate, for the rated rotational speed of 2950 rpm, in Figure 11.

**Figure 11.** Dimensionless pump curves for the rotational speed of 2950 rpm.

#### *3.4. Inline Pumped-Storage Hydropower (IPSH)*

In this stage, the numerical model was ready to be upgraded to an energy recovery system. The improvement was performed by adding a by-pass line, as shown in Figure 12. In order to examine the IPSH solution, a free surface tank (T-2) was installed in the by-pass branch that was added to the base pumping system (BPS) with the capacity of 0.032 m3. The by-pass line was equipped with a throttle control valve (TCV) working in an open or closed position to include or isolate the by-pass line. The T-2 was located at a lower elevation to generate a gravity flow from T-1 to T-2. The new IPSH system was considered as a loop system to use the previously assessed characteristics attained in the experimental loop system. It is worth mentioning that the idea is not limited to loop systems but can be adapted to a real system with direct flow condition. In a direct flow system, based on the available head at T-1 and downstream demand, the by-pass line can be activated to use the available head difference for energy generation. Hence, a turbine was considered in the by-pass line to generate energy from the gravity flow. Since WaterGEMS does not include a built-in turbine element, the general purpose valve (GPV) was used for this purpose by defining the flow-head loss curve correspondent to the turbine characteristic curves.

**Figure 12.** Scheme and visualization of the experimental set-up of the inline pumped-storage hydro (IPSH) solution.

The numerical simulation was used to assess the main variations in the IPSH system. The characteristic curves in Figure 13 were used to adjust the flow rate in the main pipe branch by changing the rotational speed of the pump and the TCV-2 opening based on the flow rate in gravity by-pass line for energy recovery. The simulations were carried out for an extended period of 24 h. Two scenarios were considered, i.e., identical and variable flow rates in the pipe system. If the flow rates in different branches of the system were equal, it led to a steady flow regime resulting in a constant water level in T-1 and T-2 (Figure 13). In this case, a gravity flow rate of 29.11 L/min existed from T-1 to T-2. To maintain this flow rate in the main pipe, a pump rotational speed of 2600 rpm and a TCV-2 opening of 72.5% were found to be appropriate based on the experimental measurements. In other words, the characteristic curves gave the ability to accurately adjust the pump working condition and valve opening percentage in order to establish a flow rate equal to the gravity flow between T-1 and T-2. Based on that, the water levels in T-1 and T-2 for the identical flow rate scenario over 24 h remained constant, as 0.50 and 0.18 m, respectively.

**Figure 13.** Dimensionless turbine characteristic curves based on numerical simulations.

In a water supply system, there was a pattern of flow demand along each 24 h. This pattern had a typical representation of each system characterization depending on the flow consumption used for water network design. Therefore, in this research, the same procedure was adopted since the flow pattern varied along the time, between rush consumption or peak hours to fewer consumptions, normally associated with the night period—the one which was also used for leak detection, since the level of consumption attained the minimum. Hence, a suitable design project for this extended period of 24 h represents a more granted solution to face flow and water level variations, head losses, leakages occurrence associated with high pressure values, along the hydraulic system and machine operation adaptation, which fit both results as the operating point. This is a complex issue that requires an extended period and is typically used in the design of water systems. Under some operating conditions, the flow rate in different branches can be variable and unequal. Then, to evaluate this scenario, a flow rate pattern of 24 h was adapted, based on a typical demand configuration, as presented in Figure 14a. A TCV-2 valve closure pattern was then calibrated to induce the desired flow rate in the hydraulic system (Figure 14b).

**Figure 14.** A real system pattern: (**a**) flow rate pattern; (**b**) valve closure pattern.

Despite the previous case of having a balance of flow rate in the whole system and constant water levels in tanks, the water level in both tanks changed with time, as shown in Figure 15. The water level variations in T-1 and T-2 were correlated, decreasing in T-1, in turbine mode and increasing in T-2, in pump mode, in a controlled optimized way between the maximum and minimum limits for tank water levels (Figure 15).

**Figure 15.** The water level in T-1 and T-2 based on the variable demand pattern.

The operating curve of the GPV valve (acting as a turbine) was calculated with the available gross head and total head losses to obtain the net head of the turbine, as presented in the dimensionless graph of Figure 13. Equation (7) was used to calculate turbine power:

$$P = \gamma Q H \eta \tag{7}$$

where *P* is the power, γ is the specific weight of the water, *Q* is the flow rate, *H* is the turbine head and η is the efficiency. Equation (7) was exploited to calculate the power for two different mentioned scenarios of constant and variable flow rates, as presented in Figure 16. The energy production of the system for a fixed flow rate of 35 L/min was 1.24 kWh, while the variable scenario led to 1.81 kWh daily energy production.

**Figure 16.** Power in the fixed and variable demand patterns.

#### **4. Dimensional Analysis and Discussion**

Experimental tests are used to predict the performance of a real device including the behavior under different operating conditions. In this case, the model was evaluated on a laboratory scale, and then the results were simulated for real conditions. The similarity theory requires principles of geometric, kinetic and dynamic parities between a model and a prototype. These affinity laws in different categories can be attained by expressing shape, size, velocity component and acting forces [37]. In this study, the scales of velocity and flow rate were calculated based on the Froude criterion, as analyzed in [38], from the length scale (λ*L*) using the following equations:

$$
\lambda\_L = \frac{L\_{\text{mod}}}{L\_{\text{pro}}} \tag{8}
$$

$$\text{Flow rate scale}: \ Q = VA \Rightarrow \lambda\_Q = \lambda\_V \lambda\_L^2 \Rightarrow \lambda\_Q = \lambda\_L^{5/2}, \tag{9}$$

$$\text{Velocity scale}: \frac{V\_{\text{mod}}}{V\_{\text{pro}}} = \frac{V\_{\text{mod}}}{\left(gL\_{\text{mod}}\right)^{1/2}} = \frac{V\_{\text{pro}}}{\left(gL\_{\text{pro}}\right)^{1/2}} \Rightarrow \frac{V\_{\text{mod}}}{V\_{\text{pro}}} = \frac{\left(gL\_{\text{mod}}\right)^{1/2}}{\left(gL\_{\text{pro}}\right)^{1/2}} \Rightarrow \lambda\_V = \lambda\_L^{1/2}.\tag{10}$$

Classic similarity laws for pumps and turbines with the same impeller diameter state that the discharge is proportional to the rotational speed, while the head is proportional to the squared rotational speed as Equation (1). Then based on [39,40], the correlation between pump and turbine mode was proved to be:

$$n\_{\rm S\_T} \text{ (in } m, \, m^3/s) = 0.8793 n\_{\rm S\_P} \tag{11}$$

$$\frac{Q\_T}{Q\_P} = 1.3595 \frac{N\_T}{N\_P} \tag{12}$$

To evaluate the results of the model in a technical approach, for a loop system where *QT* = *QP* the length scales of 20 and 50 were considered. Additionally, for geometrically similar impellers operating at the same specific speed, the affinity laws are as follows:

$$\frac{N\_{\rm mod}}{N\_{\rm pro}} = \left(\frac{H\_{\rm mod}}{H\_{\rm pro}}\right)^{1/2} \frac{D\_{\rm pro}}{D\_{\rm mod}} = \left(\frac{H\_{\rm mod}}{H\_{\rm pro}}\right)^{3/4} \left(\frac{Q\_{\rm pro}}{Q\_{\rm mod}}\right)^{1/2} = \left(\frac{P\_{\rm pro}}{P\_{\rm mod}}\right)^{1/2} \left(\frac{H\_{\rm mod}}{H\_{\rm pro}}\right)^{5/4} \tag{13}$$

or separating by specific flow, head and power:

$$\begin{array}{l} \frac{Q\_{\text{prev}}}{Q\_{\text{mod}}} = \left(\frac{N\_{\text{prev}}}{N\_{\text{mod}}}\right) \left(\frac{D\_{\text{prev}}}{D\_{\text{mod}}}\right)^{3} \\\ \frac{H\_{\text{prev}}}{H\_{\text{mod}}} = \left(\frac{N\_{\text{prev}}}{N\_{\text{mod}}}\right)^{2} \left(\frac{D\_{\text{prev}}}{D\_{\text{mod}}}\right)^{2} \\\ \frac{P\_{\text{prev}}}{P\_{\text{mod}}} = \left(\frac{N\_{\text{prev}}}{N\_{\text{mod}}}\right)^{3} \left(\frac{D\_{\text{pro}}}{D\_{\text{mod}}}\right)^{5} \end{array} \tag{14}$$

The results are presented in Table 4. The power of the model was 0.052 kW but, by upscaling, it grew to values of 1532 and 41,657 kW, for scales of 20 and 50, respectively.

**Parameter Unit Hydraulic System Turbine Impeller Turbine A**ffi**nity Laws** *QV D NT HT PT* **[m3**/**s] [m**/**s] [mm] [rpm] [m] [kW]** Model 0.60 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 0.99 25 2170 10.64 0.052 1/20 1.04 4.42 500 470 200 1532

1/50 10.31 6.99 1250 298 503 41,657

**Table 4.** Scale-up parameters for a hydraulic system and turbomachine affinity characteristic parameters with *nsT* (in m, m3/s) = 8.8.

#### **5. Conclusions**

In a base pumping system (BPS), the characteristic curves in pump and turbine modes were defined and analyzed in order to obtain the best operating conditions in water networks. The research study included experimental analyses, hydraulic simulations and optimized conditions to better define the best operating point. The experimental results were exploited to calibrate a numerical hydraulic simulator model in the WaterGEMS environment, which uses optimization in searching for the best operating conditions. This numerical model was then used to evaluate a smart conceptual energy recovery solution of an inline pumped-storage hydropower (IPSH) system. The characteristic parameters (i.e., flow rate, velocity, impeller diameter, rotational speed, head and power) of this novel model were calculated to provide a background for the energy estimation. As a result, the following main conclusions can be pointed out:


**Author Contributions:** Conceptualization—H.M.R.; Methodology and formal analysis—H.M.R., A.D., M.B.; Writing, review & editing—H.M.R., A.D., M.B. and K.A.; Data collection and validation—A.D. and M.B.; Supervision—H.M.R. and K.A.; Funding acquisition—H.M.R. and K.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by funding from REDAWN European project (www.redawn.eu).

**Acknowledgments:** The authors would like to thank CERIS (Civil Engineering, Research, and Innovation for Sustainability) Centre from Instituto Superior Técnico, Universidade de Lisboa, Portugal for providing the experimental facilities and also the European project REDAWN (Reducing Energy Dependency in Atlantic Area Water Networks) EAPA\_198/2016 from the INTERREG ATLANTIC AREA PROGRAMME 2014–2020 for the grants support.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**

*Symbols*


*Water* **2020**, *12*, 2224


#### **References**


© 2020 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/).

MDPI St. Alban-Anlage 66 4052 Basel Switzerland Tel. +41 61 683 77 34 Fax +41 61 302 89 18 www.mdpi.com

*Water* Editorial Office E-mail: water@mdpi.com www.mdpi.com/journal/water

MDPI St. Alban-Anlage 66 4052 Basel Switzerland

Tel: +41 61 683 77 34 Fax: +41 61 302 89 18