energies

Article
Underground Pumped-Storage Hydropower (UPSH)
at the Martelange Mine (Belgium): Underground
Reservoir Hydraulics
Vasileios Kitsikoudis 1, *, Pierre Archambeau 1 , Benjamin Dewals 1 , Estanislao Pujades 2 ,
Philippe Orban 3 , Alain Dassargues 3 , Michel Pirotton 1 and Sebastien Erpicum 1
1 Hydraulics in Environmental and Civil Engineering, Urban and Environmental Engineering Research Unit,
Liege University, 4000 Liege, Belgium; pierre.archambeau@uliege.be (P.A.); b.dewals@uliege.be (B.D.);
michel.pirotton@uliege.be (M.P.); s.erpicum@uliege.be (S.E.)
2 Department of Computational Hydrosystems, UFZ—Helmholtz Centre for Environmental Research,
Permoserstr. 15, 04318 Leipzig, Germany; estanislao.pujades-garnes@ufz.de
3 Hydrogeology and Environmental Geology, Urban and Environmental Engineering Research Unit,
Liege University, 4000 Liege, Belgium; p.orban@uliege.be (P.O.); alain.dassargues@uliege.be (A.D.)
* Correspondence: v.kitsikoudis@uliege.be or vkitsiko@civil.duth.gr; Tel.: +32-478-112388




Received: 22 April 2020; Accepted: 6 July 2020; Published: 8 July 2020


Abstract: The intermittent nature of most renewable energy sources requires their coupling with an
energy storage system, with pumped storage hydropower (PSH) being one popular option. However,
PSH cannot always be constructed due to topographic, environmental, and societal constraints,
among others. Underground pumped storage hydropower (UPSH) has recently gained popularity as
a viable alternative and may utilize abandoned mines for the construction of the lower reservoir in the
underground. Such underground mines may have complex geometries and the injection/pumping of
large volumes of water with high discharge could lead to uneven water level distribution over the
underground reservoir subparts. This can temporarily influence the head difference between the
upper and lower reservoirs of the UPSH, thus affecting the efficiency of the plant or inducing structural
stability problems. The present study considers an abandoned slate mine in Martelange in Southeast
Belgium as the lower, underground, reservoir of an UPSH plant and analyzes its hydraulic behavior.
The abandoned slate mine consists of nine large chambers with a total volume of about 550,000 m3 ,
whereas the maximum pumping and turbining discharges are 22.2 m3 /s. The chambers have different
size and they are interconnected with small galleries with limited discharge capacity that may hinder
the flow exchange between adjacent chambers. The objective of this study is to quantify the effect
of the connecting galleries cross-section and the chambers adequate aeration on the water level
variations in the underground reservoir, considering a possible operation scenario build upon current
electricity prices and using an original hydraulic modelling approach. The results highlight the
importance of adequate ventilation of the chambers in order to reach the same equilibrium water
level across all communicating chambers. For fully aerated chambers, the connecting galleries should
have a total cross-sectional area of at least 15 m2 to allow water flow through them without significant
restrictions and maintain similar water level at all times. Partially aerated chambers do not attain
the same water level because of the entrapped air; however, the maximum water level differences
between adjacent chambers remain relatively invariant when the total cross-sectional area of the
connecting galleries is greater than 8 m2 . The variation of hydraulic roughness of the connecting
galleries affects the water exchange through small connecting galleries but is not very influential on
water moving through galleries with large cross-sections.

Keywords: energy storage; underground pumped storage hydropower; renewable energy;

numerical modeling; water transients

Energies 2020, 13, 3512; doi:10.3390/en13143512 www.mdpi.com/journal/energies

Energies 2020, 13, 3512 2 of 16

1. Introduction
The widespread utilization of renewable energy sources such as solar and wind energy is hampered
by their intermittency and insufficient storage capacity that cannot always guarantee adequate supply
of the electricity demand [1]. As a result, electricity grids cannot yet rely solely upon renewable
energy sources [2], despite the fact that their utilization is sought for the decarbonization of electricity
networks [3]. Fossil fuels provide energy storage at low cost with high availability and easiness
in handling, and in many cases they are still preferred as the means of energy storage [4] leading
to increasing greenhouse gas emissions. To harness energy from renewable energy sources more
efficiently and to enable a transition to clean energy, solar panels and wind energy converters should
be coupled with energy storage systems. These systems are able to store excess energy during periods
of high production and low demand, and subsequently provide energy to the electricity network at
periods of high demand when the energy production is not sufficient. Pumped storage hydropower
(PSH) is the most popular technology that accommodates such energy storage [5–7] and has been
successfully utilized in numerous places all over the world (e.g., [8–10]). PSH consists of at least two
reservoirs at different elevations, which are connected with pipes or tunnels. This system stores energy
in the form of potential energy by elevating water in the upper reservoir with the aid of pumps and
generates electrical energy by releasing water to the lower reservoir and converting water kinetic
energy to electricity with turbines.
However, actual implementation of PSH may not be feasible in certain areas due to societal,
topographic, and environmental constraints (e.g., [11]). PSH reservoirs require large storage areas
that may not be available in densely populated or urbanized areas. In addition, the two reservoirs
of the PSH need to have a significant elevation difference to secure sufficient head difference for the
efficient production of electricity, which excludes flat areas as candidates for a PSH. To avoid such
limitations, at least one of the reservoirs could be located underground in cavities or in abandoned
mines and quarries. Consequently, energy can be generated and stored with underground pumped
storage hydropower (UPSH) [12,13]. While there are several options for energy storage in flat areas [14],
including surface quarry pits [15], the present study focuses on UPSH because it does not affect the
landscape, it has a minimal societal impact for the nearby communities and may rejuvenate local
economies that were most probably highly dependent on the previous local ore extraction from
the quarries or mines. UPSH has gained popularity and is considered a viable option for energy
storage [16–19]; however, the actual hydraulic behavior in the underground reservoirs must be studied
thoroughly, since the reservoir geometry and thus the hydraulic behavior of UPSH can be challenging
and more complicated compared to other solutions in flat areas.
The groundwater exchanges between the lower reservoir and the surrounding porous medium
might be significantly greater in a UPSH compared to a PSH due to the increased interface area of
the reservoir that is in contact with the surrounding medium (here after referred as the ‘aquifer’) and
likely below the water table (i.e., in the saturated zone). In addition, the sidewalls of PSH reservoirs
are sometimes waterproof, which is not especially the case in mines and quarries that could potentially
be used as underground reservoirs in UPSH. Groundwater exchanges are largely influenced by the
porosity and hydraulic conductivity of the aquifer, the characteristics of the lower reservoir, the relative
elevation of the underground water table compared to the location of the lower reservoir, and the
pump/injection cycles [20,21]. The induced gradient between the aquifer piezometric head and the
head in the lower reservoir (i.e., the abandoned mine or quarry) may affect the economic feasibility of
the UPSH system since water intrusion from the aquifer to the reservoir in between the pump/injection
cycles may lead to additional pumping of water and increase the costs [15,21]. Otherwise, the incoming
groundwater flow will reduce the head difference with the upper reservoir as well as the available
capacity of the lower reservoir and diminish the amount of water that can be transferred into the
lower reservoir, thus decreasing the generated electricity. On another hand, in case of high porosity
and hydraulic conductivity in the ground, groundwater exchanges may narrow the variation of
the water level in the underground reservoir and subsequently of the head difference between the
Energies 2020, 13, 3512 3 of 16

upper and lower reservoirs, thus facilitating the design and efficiency of the pumps and turbines [20].
In UPSH, the groundwater exchanges may also affect the water hydrochemistry and lead to adverse
environmental consequences through precipitation and dissolution of minerals and the associated
variations in pH [22], which may also affect the efficiency of the USPH plant.
Besides the water exchanges with the surrounding medium, the movement of water within the
mine or quarry is of particular interest as well [23–27]. A detailed evolution of the water levels in the
complex underground reservoir(s) needs to be predicted for feasibility analysis, as the continuous
shifting of water level in response to discharge variations during the pump/discharge cycles will
affect the head difference between the upper and lower reservoirs and possibly the turbomachinery
operation. Water level variations are also needed to assess the structural stability of the system [28].
The water level variation and the energy efficiency of the UPSH plant are particularly affected by the
geometry and the aeration conditions of the underground reservoir [23,24]. An underground reservoir
may have an overall large volume but with discharge exchange limitations at some specific points,
due to narrow cross section for instance. It may also have limited connections with the atmosphere and
thus limited possibilities for air to enter/exit the reservoir to counterbalance water volume variations.
The present study considers an abandoned slate mine in Martelange in Southeast Belgium as a
practical example of a multiple chambers underground reservoir for an UPSH plant and investigates
the evolution of water levels within a system of nine underground chambers. The large underground
chambers are successively connected with small galleries of limited cross section. A hydraulic numerical
model has been developed to analyze (a) the effect of the cross sectional area of the connecting galleries
and the subsequent inertia effects due to their limited discharge capacity and (b) the effect of aeration
of the underground chambers on the water levels. The effect of groundwater exchanges is analyzed
separately in a companion paper focusing on the same site [29].

2. Study Site
The region of Wallonia in South Belgium has been well known for its ore abundance in the
underground. The intense mining of coal, slate, iron, lead and zinc ores, etc. had a huge influence on
the economic prosperity of Wallonia for many decades. However, all mining and extraction activities
were terminated by the end of the last century and the coal and slate mines have been abandoned
since then [30]. One of those closed slate mines is located in Martelange in Southeast Belgium near
the border with Luxembourg (Figure 1). It was used here as a case study to analyze its potential to
become the lower reservoir of an UPSH. The part of the slate mine that was intended to be used as
the lower reservoir consists of nine large underground chambers interconnected with small galleries.
Despite the fact that the activities in the slate mine were terminated relatively recently, i.e., in 1995,
the actual number and exact locations of the galleries are not accurately known nor is the accurate
geometry of each underground chamber.
 Energies 2020, 13, 3512 4 of 16

Energies 2020, 13, x FOR PEER REVIEW 4 of 17

134 Figure 1. (a) Location of the Martelange mine in Belgium (map data obtained from EuroGeographics
135 Figure
and1.UN-FAO)
(a) Location
andof(b)
thea Martelange mineininthe
typical chamber Belgium (map
mine that databe
could obtained
used asfrom EuroGeographics
a reservoir ((b) courtesy of
136 and V.
UN-FAO)
Duseigne,and (b) a typical chamber in the mine that could be used as a reservoir ((b) courtesy of
http://tchorski.morkitu.org/2/martelange-02.htm).
137 V. Duseigne, http://tchorski.morkitu.org/2/martelange-02.htm).
3. UPSH System Conceptualization
138 3. UPSHSome
System Conceptualization
assumptions about the underground reservoir geometry were made based on the existing
139 drawings of the mine,about
Some assumptions to allow for a systematic
the underground analysisgeometry
reservoir of the water were flow in the
made chambers.
based The ground
on the existing
140 drawings of the mine, to allow for a systematic analysis of the water flow in the chambers. The ground has
surface is considered horizontal at an elevation of 0 m and each of the nine underground chambers
141 a rectangular
surface is consideredcuboid shape with
horizontal at anits top sideofat0−40
elevation m and m from
each the surface.
of the All nine chambers
nine underground chambersare in a
142 has a rectangular cuboid shape with its top side at −40 m from the surface. All nine chambers are inand
row, parallel to each other, and equally spaced by a 10 m distance. Each chamber has a length
143 a row,width of 15to
parallel meach
and 45 m, respectively,
other, while the
and equally spaced by height
a 10 mvaries.
distance. The bottom
Each level has
chamber of the first chamber,
a length and
144 i.e., the deeper one, reaches −150 m and subsequently the bottom level
width of 15 m and 45 m, respectively, while the height varies. The bottom level of the first chamber, of each successive chamber
145 i.e., is
theelevated by 5 reaches
deeper one, m (Figure −1502m and andTable 1). Two adjacent
subsequently the bottom chambers
level ofareeachconnected
successive bychamber
two galleries,
is
146 one atby
elevated the5 bottom
m (Figure of the chamber
2 and Table and one 60
1). Two m higher,
adjacent throughare
chambers theconnected
10 m separating
by twodistance
galleries,(Figure
one 2).
147 at theThebottom
main shaft,
of thewhich is considered
chamber and oneto60house the pumps/turbines
m higher, through the 10 is connected
m separating to the deeper (Figure
distance chamber at
2 connects the
148 its lowest point at −150 m. An aeration shaft with a rectangular cross-section
2Figure 2). The main shaft, which is considered to house the pumps/turbines is connected to the 1.5 × 1.5 m
149 deeperchamber
chamberthat at
is its
farthest
lowest away
point from the main
at −150 m. An shaft (i.e., the
aeration smallest
shaft with achamber)
rectangular to the surface (Figure
cross-section 1.5 × 2a).
150 1.5 m connects the chamber that is farthest away from the main shaft (i.e., the smallest chamber) shafts
A 2hypothetical scenario where all the chambers are fully aerated with adequately large aeration to
151 the (Figure
surface 2b) was also
(Figure 2a). examined.
A hypothetical The total volume
scenario of theallchambers
where in the Martelange
the chambers slate mine
are fully aerated withwas
152 estimated
adequately to be
large aroundshafts
aeration 550,000 m3 . The
(Figure upper
2b) was reservoir
also examined. wasTheintended to be constructed
total volume on top
of the chambers inof a
153 the Martelange slate mine was estimated to be around 550,000 m . The upper reservoir was intended of
hill 500 m from the mine at an elevation of 100 m above the3 ground with an estimated capacity
154 to be400,000 m3 . Since
constructed the of
on top chambers
a hill 500capacity
m fromisthe larger
mine than
at antheelevation
volume of of water
100 mthat
abovecanthe
be ground
transferred
withfrom
155 an estimated capacity of 400,000 m . Since the chambers capacity is larger than the volume of water 2)
the upper reservoir, the water level
3 at equilibrium conditions was kept higher than −110 m (Figure
156 thattocan maintain low water
be transferred fromvelocities
the upper nearreservoir,
the bottom theofwater
the chambers and minimize
level at equilibrium sedimentwas
conditions entrainment
kept
157 higherthatthanmay−110
be harmful
m (Figure to the pumps/turbines.
2) to maintain low water velocities near the bottom of the chambers and
158 minimize sediment entrainment that may be harmful to the pumps/turbines.
159 Table 1. Geometric characteristics of the chambers of the Martelange slate mine

Chamber Number
Chambers Dimensions
1 2 3 4 5 6 7 8 9
Bottom (m) −150 −145 −140 −135 −130 −125 −120 −115 −110
Height (m)
Energies 2020, 13, 3512 110 105 100 95 90 85 80 75 70 5 of 16

160
Figure 2. Sketch of the nine underground chambers used as underground reservoir of an underground
161 Figure
pumped 2. Sketch
storage of the nine
hydropower underground
(UPSH) for (a) chambers used as and
partially aerated underground
(b) fullyreservoir
aerated of an
chambers.
162 underground pumped storage hydropower (UPSH) for (a) partially aerated 2 and (b) fully aerated
The ventilation shaft in (a) has a rectangular cross-section with 1.5 × 1.5 m while the ventilation shafts
163 chambers. The ventilation shaft in (a) has a rectangular cross-section with 1.5 × 1.5 m2 while the
in (b) are considered large enough to secure atmospheric pressure in the chambers. The water level
164 ventilation shafts in (b) are considered large enough to secure atmospheric pressure in the chambers.
corresponds to the initial conditions of the simulations.
165 The water level corresponds to the initial conditions of the simulations.
Table 1. Geometric characteristics of the chambers of the Martelange slate mine.
166 Various geometry scenarios were examined to infer the variability of water levels in the nine
167 underground chambers. The number and location of the connecting
Chamber galleries remained the same in
Number
168 Chambers
every numericalDimensions
simulation (Figure1 2). The
2 total cross
3 sectional
4 area
5 of 6the two7connecting
8 galleries
9
169 varied from 5 to 40 m2 with a roughness height equal to 5 cm, while for some cases the roughness
170 height wasBottom −150
(m)to 20 cm, as
increased shown−145 −140
in Table 2. All−135 −130 simulated
cases were −125 −120 −115 and
for partially −110fully
Height (m) 110 105 100 95 90 85 80 75 70
171 aerated conditions.

172 Table 2.
Various geometry scenarios Examined
were scenarios
examined toininfer
numerical simulations of water levels in the nine
the variability
underground chambers. The numberCross
Number of
and Sectional
location of the connecting
Total Cross
galleries remained the same in
Roughness Height,
every Scenario
numerical simulation
Connecting(Figure 2).Area
Theoftotal
Eachcross sectional
Sectionalarea
Areaofofthe twoks,connecting
in Galleriesgalleries
varied from 5 to 40 m 2 with a roughness height2 equal to 5 cm, while for some cases the roughness
Galleries Gallery (m ) Galleries, At (m )
2 (cm)
height was1 increased to 20
2 cm, as shown in Table
2.5 2. All cases were
5 simulated for partially
5 and fully
aerated conditions.
2 2 3 6 5
3 2 3.5 7 5
4 2 Table 2. Examined scenarios
4 in numerical simulations.
8 5
Number of Cross Sectional Area of Total Cross Sectional Roughness Height, ks ,
Scenario
Connecting Galleries Each Gallery (m2 ) Area of Galleries, At (m2 ) in Galleries (cm)
1 2 2.5 5 5
2 2 3 6 5
3 2 3.5 7 5
4 2 4 8 5
5 2 4.5 9 5
6 2 5 10 5
7 2 7.5 15 5
8 2 10 20 5
9 2 20 40 5
10 2 3.5 7 20
11 2 5 10 20
Energies 2020, 13, 3512 6 of 16

4. Hydraulic Model
The hydraulic modeling of the system was carried out by interconnecting a model that simulates
the flow in the upper reservoir and a model that simulates the water movement in the underground
chambers. The upper reservoir is a large and shallow body of water and the flow was modeled based
on two-dimensional shallow water equations, i.e., depth averaged mass and momentum conservation
equations. The computational tool was provided by the academic software WOLF [31], which is a
finite volume model using an explicit scheme for time integration.
For the modeling of the lower reservoir, which comprises nine interconnected chambers, an efficient
lumped model is preferred over a detailed computationally intensive three-dimensional numerical
model. Indeed, we are interested mainly in the time evolution of the averaged water levels inside the
chambers in the context of long term operation scenarios rather than in hydrodynamic details in the
connecting galleries for instance. The lumped model consists of two mass conservation equations for
each chamber and a transient Bernoulli equation, as a simplification of the momentum conservation
equation, for the small galleries that connect the chambers. The mass conservation equation for water
in a chamber is written:
nin nout
dV X X
− Qw,i + Qw,j − µV = 0 (1)
dt
i=1 j=1

where V is the volume of water in the chamber, t is the time, nin and nout denote the number of
connecting galleries that transfer water in and out of the chamber, respectively, with discharge Qw ,
and µ is a Karush–Kuhn–Tucker multiplier [32] that takes values greater or equal to zero for constraints
on the volume of fluid in each chamber.
Likewise, the mass conservation equation for the air in the chambers is written:
nin nout
dma X X
− ρa,i Qa,i + ρa,j Qa,j − µma = 0 (2)
dt
i=1 j=1

where ma and ρα are the air mass and density, respectively, and Qa is the air discharge.
In non-aerated chambers, the pressure of the air, pa , varies with the volume of the chamber that is
occupied by water, since air is a compressible fluid. Hence, the air pressure was calculated with the
polytropic relation:
pa
C= γ (3)
ρa
where ρα = ma /Vα , with Vα being the air volume, γ is 1.4 for adiabatic conditions, which are considered
here for the relatively short periods of filling/emptying the underground reservoir, and C is a constant
equal to 78,500 (for air density equal to 1.3 kg/m3 at 1013.25 Pa pressure).
The transient Bernoulli equation for the connecting galleries, both for water and entrapped air,
is written: " ! #
dQ gS Q|Q| f L
+ + k − ∆H = 0 (4)
dt L 2gS2 D
where L is the length of the gallery, g is the acceleration of gravity, S is the cross-section of the gallery,
f is the friction coefficient calculated with Barr–Bathurst formula [33], D is the corresponding hydraulic
diameter of the gallery, k is a coefficient for local head losses (inlet and outlet), and ∆H is the head
difference at the two ends of the connecting gallery, with each head, either for water or for entrapped
air, being calculated with:
p
H= +Z (5)
ρg
where p is the fluid pressure, ρ is the fluid density, and Z is the elevation of the considered point.
The lumped model is implemented with object oriented programming and a first order implicit time
integration scheme [30] with a time step of 60 s. The numerical simulations for fully aerated chambers
214 5. Operation Scenario
215 The geometry scenarios listed in Table 2 were examined based on a 14-day discharge pattern
216 (Figure 3), which was built considering typical electricity prices variation in the region for the winter
217 of 2013.
Energies Specifically,
2020, 13, 3512 pumping of water from the underground reservoir occurs within periods with 7 of 16
218 a low cost of energy (during the night) while, on the contrary, turbining from the upper to the lower
219 reservoir took place when the price of electricity was high (noon and evening peaks). Such an
220 were conducted
operation scenarioby is
considering
typical for anfree surface
existing flow instorage
pumped chambers
schemethatonwere open
a grid withatathe top
large and making
amount of sure
221 nuclear
that and/or
the water didthermal energy
not overtop theproduction. In a future
open chambers. The porouswith underground
much more renewable
medium isenergyconsidered air
222 production,and
impervious operation scenarios
groundwater for pumped
exchanges storage will
are negligible probably
during be more fluctuating.cycles.
the pumping/turbining The
223 considered scenario is however sufficient to show that underground reservoirs used for UPSH have
224 5.additional
Operation constraints
Scenariocompared to classical surface ones, which need to be quantified during the
225 design phase.
226 The
The geometry scenarios
net mass balance withinlisted in Table
a discharge cycle2ofwere examined
24 hours based
is zero, with fullon a 14-day
exchange of a discharge
400,000 m³ pattern
227 (Figure
volume3), which was
occurring built considering
in approximately typical
5 hours electricity
(discharge prices
of 22.2 m³/s),variation in the region
once for pumping for the
and once forwinter of
228 2013. Specifically,
turbining per cycle,pumping of water allowed
with intermittencies from the underground
(Figure reservoir
3). No operations wereoccurs within
scheduled periods
in the 14 hourswith a low
229 cost of energy (during the night) while, on the contrary, turbining from the upper to the lower reservoir
that were left in a 24-hour period. Such discharge patterns were also generated for the summer and spring
230 periods
took of when
place 2013 [29];
the however, only the discharge
price of electricity was highcurve
(noonfrom
andthe winter period
evening peaks).wasSuchpresented in this scenario
an operation
231 isstudy.
typical More
fordetailed explanation
an existing pumpedon the generation
storage of the on
scheme discharge
a gridpatterns
with aislarge
provided
amountby Pujades et al. and/or
of nuclear
232 [29]. Due to the fact that in the present study the discharge cycle needed
thermal energy production. In a future with much more renewable energy production, to start with turbining, the first
operation
233 six hours of the original winter discharge time-series, corresponding to a pumping phase [29], were
scenarios for pumped storage will probably be more fluctuating. The considered scenario is however
234 moved to the end of the time-series. The water level at the beginning of each simulation was at −110 m,
sufficient to show that underground reservoirs used for UPSH have additional constraints compared
235 which means that there is water in every chamber except in chamber 9 (i.e., the shallower chamber; Figure
236 to2).classical surface ones, which need to be quantified during the design phase.

237
238 Figure 3.
Figure 3. Discharge,
Discharge,Q,Q,pattern
patternforfor
thethe
winter period
winter basedbased
period on current electricity
on current prices variation
electricity in
prices variation in
239 Belgium. Positive
Belgium. Positiveand
andnegative
negative discharges correspond
discharges to turbining
correspond and pumping,
to turbining respectively.
and pumping, respectively.

240 6. Results
The net mass balance within a discharge cycle of 24 h is zero, with full exchange of a 400,000 m3
volume occurring in approximately 5 h (discharge of 22.2 m3 /s), once for pumping and once for
turbining per cycle, with intermittencies allowed (Figure 3). No operations were scheduled in the 14 h
that were left in a 24-hour period. Such discharge patterns were also generated for the summer and
spring periods of 2013 [29]; however, only the discharge curve from the winter period was presented
in this study. More detailed explanation on the generation of the discharge patterns is provided
by Pujades et al. [29]. Due to the fact that in the present study the discharge cycle needed to start
with turbining, the first six hours of the original winter discharge time-series, corresponding to a
pumping phase [29], were moved to the end of the time-series. The water level at the beginning of
each simulation was at −110 m, which means that there is water in every chamber except in chamber 9
(i.e., the shallower chamber; Figure 2).

6. Results
The 14-day discharge scenario (Figure 3) exhibited a relative periodicity after a certain duration.
For easier interpretation of the variation of the water level across all nine chambers, only the first
80 h of the winter discharge pattern, Q, are presented in Figures 4 and 5 for partially aerated and
fully aerated underground chambers, respectively, for the three smaller cross sectional areas of the
connecting galleries (Table 2).
Water was initially injected at hour 3 into chamber 1 (i.e., the deepest chamber) through the main
shaft and the water level gradually increased in all chambers, both for partially aerated (Figure 4)
and fully aerated (Figure 5) chambers. The initial increase of the water level until hour 5 occurred
at a different rate in each chamber, with the chambers closer to the main shaft exhibiting the steeper
gradients. This is attributed to the limited discharge capacity of the connecting galleries, which was
significantly lower than the incoming discharge of 22.2 m3 /s from the main shaft. Notably, when the
water level in a chamber reached the second connecting gallery at 60 m above its bottom side, the water
 Energies 2020, 13, 3512 8 of 16

level gradient became less steep as the water exchanges between adjacent chambers were enhanced.
As the cumulative cross-sectional area of the connecting galleries increased, the discharge of water
between adjacent chambers also increased and the water levels in the different chambers increased
at a more similar rate (e.g., Figures 4c and 5c compared to Figures 4a and 5a, respectively). Indeed,
when the water injection paused temporarily after hour 5, the water levels in the chambers were
much different when the cross sections of the connecting galleries were small (Figures 4a and 5a).
Nevertheless, eventually water levels in all chambers reached an equilibrium depth after hour 5.
For fully aerated chambers, the equilibrium water level was the same in all chambers (Figure 5), but for
Energies 2020, 13, x FOR PEER REVIEW 8 of 17
partially aerated chambers, the water level in each chamber was slightly different (Figure 4) due to the
241presence The 14-day discharge scenario (Figure 3) exhibited a relative periodicity after a certain duration. at hour 10.
of entrapped air. After this initial pause, water was again injected in the chambers
242TheFor
water
easierlevel gradients
interpretation of of
thethe chambers
variation of the were not that
water level different
across now as before.
all nine chambers, only the This
first 80is due to the
243facthours
that the water
of the winterlevel was high
discharge enough
pattern, to reach in
Q, are presented the higher
Figure connecting
4 and Figure 5 forgallery
partiallyinaerated
many chambers,
244thusand fully aerated
enhancing theunderground chambers,
water exchanges respectively,
between for the three smaller cross sectional areas of
the chambers.
245 the connecting galleries (Table 2).

246
247 Figure
Figure 4. 4.Evolution
Evolution of
of the
thewater
waterlevel in the
level chambers
in the of the of
chambers underground reservoir of
the underground the UPSH
reservoir offor
the UPSH for
248 the winter discharge scenario, Q. The system is only aerated in chamber 9 and successive chambers
the winter discharge scenario, Q. The system is only aerated in chamber 9 and successive chambers
249 are connected with two galleries with total cross sectional area of (a) 5 m2, (b) 6 m2, and (c) 7 m2. The
are connected with two galleries with total cross sectional area of (a) 5 m2 , (b) 6 m2 , and (c) 7 m2 .
250 corresponding portion of the winter discharge scenario is shown in (d). The roughness height in the
251 Theconnecting
corresponding
galleriesportion of thethewinter
is 5 cm while discharge
water level scenario
is expressed with is shown
respect in (d).
to the Thesurface.
ground roughness height in
the connecting galleries is 5 cm while the water level is expressed with respect to the ground surface.
 Energies 2020, 13, 3512 9 of 16
Energies 2020, 13, x FOR PEER REVIEW 9 of 17

252
253 Figure
Figure5.5.Evolution
Evolutionofofthe water
the level
water in the
level chambers
in the of the
chambers ofunderground reservoir
the underground of the of
reservoir UPSH for
the UPSH for the
254 the winter discharge scenario, Q. The chambers are fully aerated and successive chambers
winter discharge scenario, Q. The chambers are fully aerated and successive chambers are connected are
255 connected with two galleries with total cross sectional area of 2(a) 5 m2, (b)
with two galleries with total cross sectional area of (a) 5 m , (b) 6 m2 , and 6 m2, and (c)
(c) 7 m2 . 7The
m2. The
corresponding
256 corresponding portion of the winter discharge scenario is shown in (d). The roughness height in the
portion of the winter discharge scenario is shown in (d). The roughness height in the connecting
257 connecting galleries is 5 cm while the water level is expressed with respect to the ground surface.
galleries is 5 cm while the water level is expressed with respect to the ground surface.
258 Water was initially injected at hour 3 into chamber 1 (i.e., the deepest chamber) through the main
When the water injection was again paused at hour 13, the water level in each chamber reached
259 shaft and the water level gradually increased in all chambers, both for partially aerated (Figure 4)
260 an
andequilibrium
fully aeratedlevel that
(Figure was slightly
5) chambers. Thelower
initial than theoftop
increase theside
wateroflevel
the chambers −40 m at
until hour 5atoccurred for aerated
261 chambers
a different rate in each chamber, with the chambers closer to the main shaft exhibiting the steeper 13 and
(Figure 5). For partially aerated chambers, the equilibrium water level between hours
262 19 was much
gradients. Thisdifferent in each
is attributed to thechamber (Figure 4).
limited discharge This of
capacity wasthedue to the fact
connecting that the
galleries, water
which was level had
263 risen and covered
significantly lower both connecting
than the incominggalleries
dischargeinofthe chambers
22.2 m /s from(i.e.,
3 the at theshaft.
main base and 60 mwhen
Notably, above the bottom
the
264 water
side oflevel
eachinchamber),
a chamberhence
reached thetheairsecond
in the connecting
chambers could gallerynot
at 60 m above
escape its bottom
to adjacent side, the anymore.
chambers
265 water
As level gradient
a result, becameair
the entrapped less
in steep as the water
each chamber wasexchanges
compressed between adjacent pressure.
and exerted chambers Only
were chamber
266 enhanced. As the cumulative cross-sectional area of the connecting galleries increased,
9 got completely filled with water (Figure 4) because in the partially aerated underground reservoir the discharge
267 of water between adjacent chambers also increased and the water levels in the different chambers
scenario, this specific chamber was connected to a ventilation shaft and was adequately aerated.
At hour 19, water pumping started. For relatively small cross sectional areas of the connecting
galleries (and similar to the injection phase), the chambers that were closer to the main shaft emptied
 Energies 2020, 13, 3512 10 of 16

at a faster rate as the discharge of the connecting galleries was smaller than the pumping discharge of
the main shaft (Figures 4 and 5). The lowering rate of the water level increased when the water level
became lower than the level of the upper connecting gallery and as a result the water level gradient
became steeper since the water that was pumped was much greater than the water that was provided
by the adjacent chamber. When the pumping phase was paused, e.g., at hour 24, the water levels in the
different chambers were not balanced and after some time they reached equilibrium depths. For the
fully aerated case, the equilibrium depths in the chambers were always equal to each other, regardless
of the water elevation when the pumping was paused. However, in partially aerated chambers the
elevation of the water and the associated air compressibility dictate to a large degree the equilibrium
depth in each chamber.
Figures 6 and 7 show the maximum water level differences between successive chambers across
the whole 14-day period for partially and fully aerated chambers, respectively, for the winter discharge
scenario. Both in the partially and fully aerated cases, the maximum water level difference dropped
rapidly with increasing cumulative cross section of the connecting galleries. For fully aerated chambers,
the maximum water level differences between the first two chambers with the smallest connecting
galleries were a little higher during the water pumping phase compared to the turbining phase
(Figure 7). However, the water level differences after the second chamber were slightly higher in the
turbining phase, most evidently for the smaller cross-sections. The maximum water level differences in
fully aerated chambers were always greater for chambers that were closer to the main shaft, which was
connected to chamber 1; however, for total cross sectional areas of the connecting galleries greater
than 15 m2 , the differences became rather negligible. Notably, the maximum water level difference
between the first and last chamber in the fully aerated case could be expressed as a power function of
the total cross-sectional area of the connecting galleries, both for the turbining and the pumping phase
Energies (Figure
2020, 13, x8).
FOR PEER REVIEW 11 of 17

315
316 Figure Figure 6. Maximum
6. Maximum differences
differences of wateroflevel
water(WL)
levelin(WL) in successive
successive chambers chambers of the underground
of the underground
317 reservoir
reservoir of the for
of the UPSH UPSH for aofrange
a range total of totalsectional
cross cross sectional
areas, Aareas, At ,connecting
t, of the of the connecting
galleriesgalleries
when when
318 only chamber 9 is aerated for the winter discharge scenario. Successive chambers are connected with with
only chamber 9 is aerated for the winter discharge scenario. Successive chambers are connected
319 two galleries
two galleries with roughness
with roughness heighttoequal
height equal 5 cm.to 5 cm.

320 For partially

For partially aeratedaerated
chambers,chambers,
the waterthelevel
waterdifferences
level differences
between between
adjacentadjacent
chambers chambers exhibited
exhibited
321 a morea complicated
more complicatedpatternpattern
compared compared
to fullyto aerated
fully aerated
chambers.chambers.
Figure Figure
6 shows 6 shows
that forthat for small
small
2 , the water level differences between
322 connecting galleries with total cross sectional area up to 8 m
connecting galleries with total cross sectional area up to 8 m , the water level differences between
2

323 adjacentadjacent
chambers chambers
initiallyinitially
decreaseddecreased as the chambers
as the chambers becamebecame more distant
more distant from the from
maintheshaft
mainandshaft and
324 after a certain point the water level differences increased. On the contrary, the
after a certain point the water level differences increased. On the contrary, the water level differences water level differences
325 between between chambers
chambers for for connecting
connecting gallerieswith
galleries with cross
crosssections
sections larger 8 m2 increased
thanthan
larger monotonically
8 m2 increased
326 with increasing
monotonically distance distance
with increasing from thefrom mainthe shaft.
mainThe large
shaft. Theincrease in the last
large increase in pair of chambers
the last pair of (i.e.,
327 chambers 8 and 9) was due to the ventilation shaft that was connected
chambers (i.e., chambers 8 and 9) was due to the ventilation shaft that was connected to chamber to chamber 9 allowing to 9become
328 fully filled with water. For partially aerated chambers, some of the
allowing to become fully filled with water. For partially aerated chambers, some of the maximummaximum water level differences
329 water level differences occurred during equilibrium conditions, thus Figure 6 did not examine
330 separately the turbining and pumping phases like Figure 7 for the fully aerated chambers.
322 connecting galleries with total cross sectional area up to 8 m2, the water level differences between
323 adjacent chambers initially decreased as the chambers became more distant from the main shaft and
324 after a certain point the water level differences increased. On the contrary, the water level differences
325 between chambers for connecting galleries with cross sections larger than 8 m2 increased
326 monotonically with
Energies 2020, 13, 3512increasing distance from the main shaft. The large increase in the last pair 11
ofof 16
327 chambers (i.e., chambers 8 and 9) was due to the ventilation shaft that was connected to chamber 9
328 allowing to become fully filled with water. For partially aerated chambers, some of the maximum
329 occurred
water during equilibrium
level differences occurredconditions, thus Figureconditions,
during equilibrium 6 did not examine separately
thus Figure 6 didthe
notturbining
examineand
330 pumping phases like Figure 7 for the fully aerated chambers.
separately the turbining and pumping phases like Figure 7 for the fully aerated chambers.

331
332 Figure
Figure 7. Maximum
7. Maximum differences
differences of water
of water levellevel
(WL)(WL) in successive
in successive chambers
chambers of theof the underground
underground
333 reservoir
reservoir of theof UPSH
the UPSH during
during (a) turbining
(a) turbining and and (b) pumping
(b) pumping phases
phases for afor a range
range of total
of total crosscross sectional
sectional
334 areas, A , of the connecting galleries when the chambers are fully aerated for the
areas, At, of tthe connecting galleries when the chambers are fully aerated for the winter discharge winter discharge
335 Energies scenario.
2020,
scenario. 13, Successive
x FOR
Successive PEER chambers
REVIEW
chambers are connected
are connected withwith
two two galleries
galleries withwith roughness
roughness height
height equal
equal to 5 to
cm.5 12
cm.of 17

336
337 Figure
Figure 8. 8.
Maximum
Maximum difference
differenceofofwater
waterlevel
level(WL)
(WL) between chambers 11 and
between chambers and99during
during(a)(a)turbining
turbining
and
338 and(b)(b) pumping
pumping phases
phases forfor a range
a range ofof total
total cross
cross sectionalareas,
sectional areas,AtA, tof
, ofthe
theconnecting
connectinggalleries
gallerieswhen
whenthe
339 thechambers
chambersare arefully
fullyaerated
aeratedfor for the
the winter
winter discharge
discharge scenario.
scenario. Successive
Successive chambers
chambers areare connected
connected with
340 with
two two galleries
galleries withwith roughness
roughness height
height equal
equal to 5tocm.
5 cm.

341 TheThe effect

effect of of
thethe hydraulic
hydraulic roughness
roughness of of
thethe connecting
connecting galleries
galleries ononthethe water
water level
level differences
differences
342 between
between successive
successive chambers
chambers was
was additionally
additionally analyzed.
analyzed. SoSofar,far,
a 5acm5 cm value
value of the
of the roughness
roughness height,
height,
343 k
ks, of, of the connecting galleries was considered. An
s the connecting galleries was considered. An increase of ks to increase of k to 20 cm has been examined.
s 20 cm has been examined. The effect The effect
344 of of increased
increased roughness
roughness in in
thethe connecting
connecting galleries
galleries onon maximum
maximum water
water level
level differences
differences waswas more
more
345 prominent for the chambers closer to the main shaft, both for partially
prominent for the chambers closer to the main shaft, both for partially aerated (Figure 9) and fully aerated (Figure 9) and fully
346 aerated
aerated (Figure
(Figure 10)10) chambers.
chambers. TheThe induced
induced differences
differences forfor
a 7a m 2 2
7 mtotal
total cross-sectional
cross-sectional areaarea
of of
thethe
347 connecting
connecting galleries
galleries exceeded
exceeded one one meter
meter forfor
thethe first
first twotwo chambers
chambers andand became
became negligible
negligible at at
thethe
348 chambers away from the main shaft. When the total cross sectional
chambers away from the main shaft. When the total cross sectional area of the connecting galleriesarea of the connecting galleries
349 increased
increased from
from 7 to
7 to 1010 m2m
2 , the effect of the increasing roughness in the connecting galleries became
, the effect of the increasing roughness in the connecting galleries became
350 much
much less
less prominent,
prominent, especially
especially whenwhenthethe chambers
chambers were
were only
only partially
partially aerated
aerated (Figure
(Figure 9).9).
345 prominent for the chambers closer to the main shaft, both for partially aerated (Figure 9) and fully
346 aerated (Figure 10) chambers. The induced differences for a 7 m2 total cross-sectional area of the
347 connecting galleries exceeded one meter for the first two chambers and became negligible at the
348 chambers away from the main shaft. When the total cross sectional area of the connecting galleries
349 increased from 7 to 10 m2, the effect of the increasing roughness in the connecting galleries became
Energies 2020, 13, 3512 12 of 16
350 much less prominent, especially when the chambers were only partially aerated (Figure 9).

351
352 Figure
Figure 9. 9. Maximum
Maximum differences
differences of of
thethe water
water level
level (WL)
(WL) in in successive
successive chambers
chambers of of
thethe underground
underground
353 reservoir
reservoir of of
thethe UPSH
UPSH forfor different
different roughness
roughness heights, ks,kand
heights, s , and total
total cross
cross sectional
sectional At,Aof
areas,
areas, t , of
thethe
354 connecting
connecting galleries
galleries when
when only
only chamber
chamber 9 is
9 is aerated
aerated forfor
thethe winter
winter dischargescenario.
discharge scenario.Successive
Successive
355 Energies chambers
2020,
chambers 13, areare
x FOR connected
PEER REVIEW
connected with
with twotwo galleries.
galleries. 13 of 17

356
357 Figure
Figure 10.10. Maximum
Maximum differences
differences of of thethe water
water level
level (WL)
(WL) in in successive
successive chambers
chambers of of
thethe underground
underground
358 reservoir
reservoir of of the
the UPSHduring
UPSH during(a)(a)turbining
turbiningand and(b)
(b)pumping
pumpingphase
phasefor
for different heights, ks ,
different roughness heights,
359 ks, and
and total
total cross
crosssectional areas,AAt ,t, of
sectionalareas, ofthe
theconnecting
connectinggalleries
gallerieswhen
whenthe
thechambers
chambersare arefully
fullyaerated
aeratedfor
360 forthe
thewinter
winterdischarge
dischargescenario.
scenario.Successive
Successivechambers
chambersareareconnected
connectedwith
withtwo
twogalleries.
galleries.

7. Discussion
361 7. Discussion
The efficient utilization of an UPSH plant requires accurate predictions of the water levels and the
362 The efficient utilization of an UPSH plant requires accurate predictions of the water levels and
associated hydraulic heads in the complex underground reservoir for the determination of potential
363 the associated hydraulic heads in the complex underground reservoir for the determination of
energy storage through pumping from the lower to the upper reservoir and for the estimation of the
364 potential energy storage through pumping from the lower to the upper reservoir and for the
remaining volume capacity for electricity generation through discharging from the upper to the lower
365 estimation of the remaining volume capacity for electricity generation through discharging from the
reservoir. The use of abandoned mines as lower reservoirs in UPSH plants makes the prediction of
366 upper to the lower reservoir. The use of abandoned mines as lower reservoirs in UPSH plants makes
head difference between the upper and lower reservoirs difficult for three reasons. First, because of the
367 the prediction of head difference between the upper and lower reservoirs difficult for three reasons.
constraints of ore location and excavation stability, the geometry of a mine is complex and the available
368 First, because of the constraints of ore location and excavation stability, the geometry of a mine is
volume to store water is not concentrated in a single large cavity. Consequently, the water level in
369 complex and the available volume to store water is not concentrated in a single large cavity.
different parts of the mine may exhibit strong differences when water is pumped/injected at a single
370 Consequently, the water level in different parts of the mine may exhibit strong differences when
location, thus impacting the head difference with the upper reservoir. Second, in an underground
371 water is pumped/injected at a single location, thus impacting the head difference with the upper
cavity, there is no infinite connection to the atmosphere. This means that any modification of the water
372 reservoir. Second, in an underground cavity, there is no infinite connection to the atmosphere. This
volume in the cavity needs to be compensated by a variation of the volume of air in the cavity. Finally,
373 means that any modification of the water volume in the cavity needs to be compensated by a variation
groundwater exchanges occur with the surrounding medium. The first two factors were addressed in
374 of the volume of air in the cavity. Finally, groundwater exchanges occur with the surrounding
the present study and the third one in Pujades et al. [29], considering the same test case.
375 medium. The first two factors were addressed in the present study and the third one in Pujades et al.
The abandoned slate mine in Martelange that served here as a case study comprises large chambers
376 [29], considering the same test case.
connected with small galleries with limited discharge capacity. In case the connecting galleries were
377 The abandoned slate mine in Martelange that served here as a case study comprises large
378 chambers connected with small galleries with limited discharge capacity. In case the connecting
379 galleries were too narrow, the incoming discharge from the main shaft was significantly greater than
380 the combined cumulative discharge of the connecting galleries and consequently the hydraulic head
381 within the first chamber was significantly increased. This reduced the head difference between the
Energies 2020, 13, 3512 13 of 16

too narrow, the incoming discharge from the main shaft was significantly greater than the combined
cumulative discharge of the connecting galleries and consequently the hydraulic head within the first
chamber was significantly increased. This reduced the head difference between the upper and lower
reservoirs, and decreased the UPSH plant efficiency. To fully exploit the elevation difference between
the upper and the lower reservoir, drilling of additional connecting galleries or widening of the existing
ones is effective in reducing the water level differences between the chambers. The reduction of
water level difference from side to side of (between chambers) pillars will also restrict the exposure
to bending forces. However, such works will increase the investment cost and may also weaken the
pillars separating the chambers.
Another option is to fill the lower reservoir by steps, with breaks in between injections of large
portions of water from the upper reservoir, so that the water level becomes uniform across all the
interconnected chambers and the hydraulic head in the chamber that is connected to the main shaft is
reduced. Such an operating way is however not compatible with the level of flexibility required by
energy storage systems. With the operation scenario considered in this study, build upon classical
use of an existing pumped storage scheme connected to a grid with a large amount of nuclear and/or
thermal energy production, the results presented above already show prohibitive water elevation
variation in the underground reservoir. In a future with much more renewable energy production,
operation scenarios for pumped storage will be more fluctuating and the problem will be exacerbated.
Similarly, the problem of underground reservoir aeration is crucial. Insufficient aeration can affect
significantly the water levels variation in the reservoir compared to a lower reservoir with atmospheric
pressure. Menendez et al. [24] showed that entrapped air due to inadequate aeration of an abandoned
coal mine reduces significantly the generation of electricity. However, the underground reservoir in
their study had a different geometry and the flow was not constrained by narrow galleries with limited
discharge capacity such as those in the present study. Air flow is subject to the same constraint as
water flow in limited cross sections. The significant costs of opening additional aeration shafts and
connecting galleries, or widening the existing ones, should be compared to the efficiency gain. Different
technical solutions could be assessed to facilitate air exchange between the chambers and the surface
and between adjacent chambers, such as the drilling of several small boreholes instead of a large
aeration shaft or the installation of air pipes in the galleries connecting adjacent chambers, respectively.
Herein, the porous underground medium was considered air impervious; however, in reality there
may be some air leakages that depend on the air pressure in the chambers and on the characteristics of
the underground medium. This could decrease the amplitude of air pressure variations and then have
an effect on the water level differences between successive chambers. The simulations presented in
this paper consider the two extreme scenarios about air behavior and provide the envelope of its effect
on water level differences between successive chambers.
Pujades et al. [29] considered the construction of the same UPSH plant in Martelange and
investigated the groundwater exchanges problem with numerical simulation over a period of a
year with a 15 min time interval. The operation scenario they used was the same as in the present
study. Although the present paper and the paper by Pujades et al. [29] investigate the same case
study, the coupling of the two numerical models to analyze simultaneously the hydraulics within
the chambers and the groundwater exchanges would lead to a prohibitive computational cost. Thus,
the two studies can be considered complementary to each other since they focus on different time-scales.
Pujades et al. [29] showed that over short time periods the groundwater exchanges can be negligible
compared to the pumping/turbining cycles from the upper reservoir in the surface, since the maximum
groundwater inflow rate was 0.37 m3 /s, which is much lower than the maximum pumping/turbining
discharge rate of 22.2 m3 /s from the main shaft. When combining the findings from the two studies, it can
be inferred that the head in the underground reservoir will slowly increase, which will lead to reduced
production of electricity, unless the accumulating groundwater inflows are periodically removed.
Nevertheless, in case the natural piezometric head was lower, the inflow–outflow groundwater
exchanges would be more balanced [29].
Energies 2020, 13, 3512 14 of 16

8. Conclusions
Energy production is shifting to renewable energy sources for the reduction of carbon emissions.
The intermittent nature of most renewable energy sources requires their coupling with efficient
energy storage systems of large capacity, such as PSH plants. To overcome topographic, societal and
environmental limitations associated with the construction of new PSH plants, the option of using
abandoned mines for the construction of the lower reservoir under the ground with an UPSH plant
appears as an attractive alternative. However, the use of abandoned mines as lower reservoirs in
UPSH plants makes the prediction of the plant operation difficult for several reasons related to the
complex geometry of the available underground volume and its aeration conditions. In particular,
in this study, the application of an original hydraulic modelling approach to the specific case of a slate
mine in Belgium showed that the water level in the underground reservoir is unlikely to be constant
across the whole reservoir, affecting thus significantly the head difference between the upper and lower
reservoirs as well as possibly undermining the underground reservoir stability.
It can be inferred that each abandoned mine that is considered a viable option for an UPSH
plant may represent a unique case with its own peculiarities. The location of the mine, its geometry,
the underground properties, the type of mining activities when the mine was functional, and the
aimed energy production lead to a combination of influencing parameters that is probably unique
for each mine. A general model for UPSH project feasibility studies should therefore be based on
a cross-disciplinary approach with intertwined hydraulic, geotechnical, and economical modeling.
From a hydraulic engineering standpoint, the sought cross-sectional area of the limiting reservoir
areas should be large enough to supply enough water to the chamber that is connected to the main
shaft during pumping phase and convey large portions of water to the neighboring chambers (i.e.,
maintain a uniform water level across all chambers at all times) during the turbining phase to secure
uninterrupted operations and maximize the efficiency of the UPSH plant. However, in such projects
the hydraulic modeling of underground reservoirs will be inevitably subject to additional restrictions
that may constrain the optimal hydraulic design and the desired widening of connecting tunnels
or aeration shafts may not be recommended in order to secure the stability of the cavity, reduce the
costs, and maximize the net revenue of the plant. The same problem arises with the air volume
possibly entrapped in the underground reservoir, which could significantly alter the water movements.
Development of innovative cost-efficient solutions to these problems is required to enable the use
of existing underground cavities as reservoirs for UPHS plants. The hydraulic modelling approach
presented in this paper offers a quick evaluation of the effect of such solutions.

Author Contributions: Conceptualization, V.K., P.A., S.E.; methodology, V.K., P.A., S.E.; software, P.A., M.P.;
investigation, V.K., P.A., B.D., E.P., P.O., A.D., M.P., S.E.; writing—original draft preparation, V.K., P.A., B.D.,
E.P., P.O., A.D., M.P., S.E.; writing—review and editing, V.K., P.A., B.D., E.P., P.O., A.D., M.P., S.E.; supervision,
S.E.; funding acquisition, E.P., A.D., M.P., S.E. All authors have read and agreed to the published version of
the manuscript.
Funding: This research was partly funded by the Public Service of Wallonia—Department of Energy and
Sustainable Building through the Smartwater project, the University of Liège and the EU through the Marie Curie
BeIPD-COFUND postdoctoral fellowship program (2014–2016 “Fellows from FP7-MSCA-COFUND, 600405”
and the Fonds de la Recherche Scientifique - FNRS under Grant(s) n◦ R.8003.18 (IC4WATER—Joint WATER JPI
Call 2017)).
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.

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