sign in sign up
<<
Home , Hydroelectricity, Hydropower, Martelange

Article Underground Pumped-Storage (UPSH) at the Martelange Mine (): Underground 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 , Urban and Environmental Engineering Research Unit, Liege University, 4000 Liege, Belgium; [email protected] (P.A.); [email protected] (B.D.); [email protected] (M.P.); [email protected] (S.E.) 2 Department of Computational Hydrosystems, UFZ—Helmholtz Centre for Environmental Research, Permoserstr. 15, 04318 Leipzig, ; [email protected] 3 Hydrogeology and Environmental Geology, Urban and Environmental Engineering Research Unit, Liege University, 4000 Liege, Belgium; [email protected] (P.O.); [email protected] (A.D.) * Correspondence: [email protected] or [email protected]; Tel.: +32-478-112388

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

Abstract: The intermittent nature of most renewable sources requires their coupling with an 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 with high discharge could to uneven water level distribution over the underground reservoir subparts. This can temporarily influence the head difference between the upper and lower of the UPSH, thus affecting the efficiency of the 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 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 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; ; 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 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 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 . This system stores energy in the form of by elevating water in the upper reservoir with the aid of pumps and generates by releasing water to the lower reservoir and converting water to electricity with . 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 , 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 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 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 ‘’) 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 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 focusing on the same site [29].

2. Study Site The region of in South Belgium has been well known for its ore abundance in the underground. The intense of , slate, iron, lead and zinc , 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 (Figure1). 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 Figureand 1. UN-FAO) (a) Location and of (b the) a Martelange typical chamber mine in in the Belgiu minem that(map could data be obtained used as from a reservoir EuroGeographics ((b) courtesy of 136 and V.UN-FAO) Duseigne, and http: (b)// atchorski.morkitu.org typical chamber in the/2/martelange-02.htm mine that could be). used as a reservoir ((b) courtesy of 137 V. Duseigne, http://tchorski.morkitu.org/2/martelange-02.htm). 3. UPSH System Conceptualization 138 3. UPSHSome System assumptions Conceptualization about the underground reservoir geometry were made based on the existing 139 drawingsSome assumptions of the mine, about to allow the underground for a systematic reservoir analysis geometry of the water were flow made in the based chambers. on the existing The ground 140 drawingssurface of is the considered mine, to allow horizontal for a systematic at an elevation analysis of 0 mof andthe water each of flow the in nine the underground chambers. The chambers ground has a rectangular cuboid shape with its top side at 40 m from the surface. All nine chambers are in a 141 surface is considered horizontal at an elevation of 0− m and each of the nine underground chambers 142 has row,a rectangular parallel tocuboid each other,shape andwith equally its top spacedside at − by40 am 10 from m distance. the surface. Each All chamber nine chambers has a length are in and 143 a row,width parallel of 15 to m each and 45other, m, respectively,and equally spaced while the by heighta 10 m varies.distance. The Each bottom chamber level has of the a length first chamber, and i.e., the deeper one, reaches 150 m and subsequently the bottom level of each successive chamber 144 width of 15 m and 45 m, respectively,− while the height varies. The bottom level of the first chamber, 145 i.e., isthe elevated deeper one, by 5 reaches m (Figure −1502 and m and Table subsequently1). Two adjacent the bott chambersom level of are each connected successive by twochamber galleries, is 146 elevatedone at by the 5 bottomm (Figure of the2 and chamber Table and1). Two one 60adjacent m higher, chambers through are the connected 10 m separating by two distance galleries, (Figure one 2). 147 at theThe bottom main shaft, of the which chamber is considered and one to60 house m higher, the pumps through/turbines the 10 is connectedm separating to the distance deeper (Figure chamber at its lowest point at 150 m. An aeration shaft with a rectangular cross-section 1.5 1.5 m2 connects the 148 2Figure 2). The main −shaft, which is considered to house the pumps/turbines is ×connected to the 149 deeperchamber chamber that at is its farthest lowest away point from at − the150 mainm. An shaft aeration (i.e., theshaft smallest with a chamber)rectangular to thecross-section surface (Figure 1.5 × 2a). 150 1.5 mA2hypothetical connects the scenario chamber where that is all farthest the chambers away from are fully the main aerated shaft with (i.e., adequately the smallest large chamber) aeration shaftsto 151 the (Figuresurface2 b)(Figure was also 2a). examined. A hypothetical The total scenario volume where of the all chambers the chambers in the Martelangeare fully aerated slate mine with was 3 152 adequatelyestimated large to beaeration around shafts 550,000 (Figure m . The2b) was upper also reservoir examined. was The intended total volume to be constructed of the chambers on top in of a 153 the Martelangehill 500 m from slatethe mine mine was at estimated an elevation to be of around 100 m 550,000 abovethe m3.ground The upper with reservoir an estimated was intended capacity of 3 154 to be400,000 constructed m . Since on top the of chambers a hill 500 capacity m from is the larger mine than at an the elevation volume ofof water100 m thatabove can the be ground transferred with from the upper reservoir, the water level3 at equilibrium conditions was kept higher than 110 m (Figure2) 155 an estimated capacity of 400,000 m . Since the chambers capacity is larger than the volume− of water 156 thatto can maintain be transferred low water from velocities the upper near reservoir, the bottom the of water the chambers level at equilibrium and minimize conditions sediment was entrainment kept 157 higherthat than may − be110 harmful m (Figure to the2) to pumps maintain/turbines. low water velocities near the bottom of the chambers and 158 minimize sediment entrainment that may be harmful to the pumps/turbines.

Energies 2020, 13, x FOR PEER REVIEW 5 of 17

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 Energies 2020, 13, 3512Height (m) 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 pumpedFigure storage 2. Sketch hydropower of the nine (UPSH) underground for (a) chambers partially aeratedused as andunderground (b) fully reservoir aerated of chambers. an 162 The ventilationunderground shaft pumped in (a) hasstorage a rectangular hydropower cross-section (UPSH) for with(a) partially 1.5 1.5 aerated m2 while and the(b) ventilationfully aerated 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 theChamber connecting Number galleries remained the same in Chambers Dimensions 168 every numerical simulation (Figure1 2). The 2 total 3cross sectional 4 5area of 6the two 7 connecting 8 galleries 9 169 varied from 5 to 40 m2 with a roughness height equal to 5 cm, while for some cases the roughness Bottom (m) 150 145 140 135 130 125 120 115 110 170 height was increased to 20 cm, as− shown− in Table− 2. All− cases were− simulated− − for partially− and− fully Height (m) 110 105 100 95 90 85 80 75 70 171 aerated conditions.

172 Various geometry scenariosTable 2. were Examined examined scenarios to in infer numerical the variabilitysimulations of water levels in the nine underground chambers.Number The of numberCross and Sectional location of the connectingTotal Cross galleries Roughness remained Height, the same in everyScenario numerical simulationConnecting (Figure 2).Area The of total Each cross sectionalSectional area Area of of the twoks connecting, in Galleries galleries 2 varied from 5 to 40 mGallerieswith a roughnessGallery height (m2) equal toGalleries, 5 cm, while At (m for2) some cases(cm) the roughness height was1 increased to2 20 cm, as shown in 2.5 Table 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 2 2 Connecting Galleries Each Gallery (m ) Area of Galleries, At (m ) 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 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: n n dV Xin Xout Q + Q µV = 0 (1) dt − w,i w,j − 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 ρ Q + ρ Q µma = 0 (2) dt − a,i a,i a,j a,j − i=1 j=1 where ma and ρα are the air mass and , 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 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 Energies 2020, 13, x FOR PEER REVIEW 7 of 17

202 where L is the length of the gallery, g is the acceleration of gravity, S is the cross-section of the gallery, 203 f is the friction coefficient calculated with Barr–Bathurst formula [33], D is the corresponding 204 hydraulic diameter of the gallery, k is a coefficient for local head losses (inlet and outlet), and ΔH is 205 the head difference at the two ends of the connecting gallery, with each head, either for water or for 206 entrapped air, being calculated with:

p HZ=+ (5) ρg

207 where p is the fluid pressure, ρ is the fluid density, and Z is the elevation of the considered point. 208 The lumped model is implemented with object oriented programming and a first order implicit 209 time integration scheme [30] with a time step of 60 s. The numerical simulations for fully aerated 210 chambers were conducted by considering free surface flow in chambers that were open at the top 211 and making sure that the water did not overtop the open chambers. The porous underground 212 medium is considered air impervious and groundwater exchanges are negligible during the 213 pumping/turbining cycles.

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 Energiesof 2013.2020 Specifically,, 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 wereoperation conducted scenario by is considering typical for an free existing surface pumped flow in storage chambers scheme that on were a grid open with at a thelarge top amount and making of sure 221 thatnuclear the waterand/or did thermal not overtop energy the production. open chambers. In a future The porous with undergroundmuch more renewable medium isenergy considered air 222 imperviousproduction, andoperation groundwater scenarios exchanges for pumped are negligiblestorage will during probably the pumpingbe more /turbiningfluctuating. cycles. The 223 considered scenario is however sufficient to show that underground reservoirs used for UPSH have 224 5.additional Operation constraints Scenario compared to classical surface ones, which need to be quantified during the 225 design phase. 226 TheThe geometrynet mass balance scenarios within listed a discharge in Table cycle2 ofwere 24 hours examined is zero, with based full on exchange a 14-day of a discharge 400,000 m³ pattern 227 (Figurevolume3 ),occurring which was in approximately built considering 5 hours typical (dischar electricityge of 22.2 prices m³/s), variation once for inpumping the region and foronce the for winter of 228 2013.turbining Specifically, per cycle,pumping with intermitte of waterncies allowed from the (Figure underground 3). No operatio reservoirns were occurs scheduled within in the periods 14 hours with a low 229 costthat of were energy left in (during a 24-hour the period. night) Such while, discharge on the patterns contrary, were turbining also generated from for the the upper summer to theandlower reservoir 230 tookperiods place of when2013 [29]; the however, price of electricityonly the discharge was high curv (noone from and the evening winter period peaks). was Such presented an operation in this scenario 231 isstudy. typical More for detailed an existing explanation pumped on the storage generation scheme of the ondischarge a grid patte withrns a is large provided amount by Pujades of nuclear et al. and/or 232 thermal[29]. Due energy to the fact production. that in the present In a future study the with disc muchharge morecycle needed renewable to start energy with turbining, production, 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 FigureFigure 3.3. Discharge, QQ, pattern, pattern for for the the winter winter period period based based on current on current electricity electricity prices variation prices variation in in 239 Belgium.Belgium. Positive and and negative negative discharges discharges corre correspondspond to turbining to turbining and pumping, and pumping, respectively. respectively.

240 6. ResultsThe 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 (Figure3). 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; Figure2).

6. Results The 14-day discharge scenario (Figure3) 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 Figures4 and5 for partially aerated and fully aerated underground chambers, respectively, for the three smaller cross sectional areas of the connecting galleries (Table2). 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 (Figure4) and fully aerated (Figure5) 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., Figures4c and5c compared to Figures4a and5a, 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 (Figures4a and5a). 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 (Figure5), but for partiallyEnergies aerated2020, 13, x FOR chambers, PEER REVIEW the water level in each chamber was slightly different (Figure8 of 174) due to the

241presence The of 14-day entrapped discharge air. Afterscenario this (Figure initial 3) pause,exhibited water a relative was periodicity again injected after a incertain the chambersduration. at hour 10. 242The For water easier level interpretation gradients of ofthe the variation chambers of the werewater level not thatacross di allfferent nine chambers, now asbefore. only the Thisfirst 80 is due to the 243fact hours that theof the water winter level discharge was highpattern, enough Q, are presented to reach in the Figure higher 4 and connecting Figure 5 for gallery partially in aerated many chambers, 244thus and enhancing fully aerated the underground water exchanges chambers, between respectively the chambers., for the three smaller cross sectional areas of 245 the connecting galleries (Table 2).

246 247 FigureFigure 4. 4.Evolution Evolution of the the water water level level in the in thechambers chambers of the ofunderground the underground reservoir of reservoir the UPSH of for 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 galleries portion is 5 cm while of the the winter water level discharge is expressed scenario with isrespect shown to the in (groundd). The surface. 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 5. 5. EvolutionEvolution of ofthe the water water level level in the in thechambers chambers of the of underground the underground reservoir reservoir of the ofUPSH the UPSHfor for the 254 winterthe winter discharge discharge scenario, scenario,Q .Q The. The chambers chambers are are fully fully aerated aerated and and successive successive chambers chambers areare connected 2 2 2 255 withconnected two gallerieswith two withgalleries total with cross total sectional cross sectional area of (areaa) 5 of m 2(,(a) b5) m 6 m, (2b,) and6 m (,c )and 7 m (c2). 7 The m . corresponding The 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) an equilibrium level that was slightly lower than the top side of the chambers at 40 m for aerated 260 and fully aerated (Figure 5) chambers. The initial increase of the water level until hour 5 occurred− at 261 chambersa different (Figurerate in 5each). For chamber, partially with aerated the chambers chambers, closer the to equilibrium the main shaft water exhibiting level between the steeper hours 13 and 262 19gradients. was much This diisff attributederent in eachto the chamber limited discharge (Figure4 capacity). This wasof the due connecting to the fact galleries, that the which water was level had 263 risensignificantly and covered lower boththan the connecting incoming galleries discharge in of the 22.2 chambers m3/s from (i.e., the atmain the shaft. base andNotably, 60 m when above the the bottom 264 sidewater of level each in chamber), a chamber hence reached the the air second in the connecting chambers couldgallery not at 60 escape m above to adjacentits bottom chambers side, the anymore. 265 Aswater a result, level gradient the entrapped became air less in steep each chamberas the water was exchanges compressed between and exertedadjacent pressure.chambers Onlywere chamber 266 9enhanced. got completely As the cumulative filled with cross- watersectional (Figure area4) becauseof the connecting in the partially galleries aeratedincreased, underground the discharge reservoir 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 (Figures4 and5). 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. Figures6 and7 show the maximum water level di fferences 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 (Figure7). However, the water level di fferences 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 function of the total cross-sectional area of the connecting galleries, both for the turbining and the pumping phase Energies (Figure2020, 13, 8x). FOR PEER REVIEW 11 of 17

315 316 Figure Figure6. Maximum 6. Maximum differences diff erencesof water of level water (WL) level in (WL) successive in successive chambers chambers of the underground of the underground 317 reservoirreservoir of the UPSH of the for UPSH a range for aof range total ofcross total sectional cross sectional areas, A areas,t, of theAt ,connecting of the connecting galleries galleries when when 318 only chamberonly chamber 9 is aerated 9 is aeratedfor the winter for the discharge winter discharge scenario. scenario. Successive Successive chambers chambers are connected are connected with with 319 two galleriestwo galleries with roughness with roughness height equal height to equal 5 cm. to 5 cm.

320 For partiallyFor partially aerated aerated chambers, chambers, the water the level water di levelfferences differences between between adjacent adjacent chambers chambers exhibited exhibited 321 a morea complicated more complicated pattern pattern compared compared to fully to aerated fully aerated chambers. chambers. Figure Figure6 shows6 shows that for that small for small 2 322 connectingconnecting galleries galleries with total with cross total sectional cross sectional area up area to 8 up m2 to, the 8 m water, the level water differences level differences between between 323 adjacentadjacent chambers chambers initially initially decreased decreased as the chambe as the chambersrs became became more distant more distant from the from main the shaft main and shaft and 324 after a aftercertain a certainpoint the point water the level water differences level differences increased. increased. On the Oncontrary, the contrary, the water the level water differences level differences 2 325 betweenbetween chambers chambers for forconnecting connecting galleries galleries with with crosscross sections sections larger larger than than 8 m increased8 m2 increased monotonically 326 monotonicallywith increasing with increasing distance distance from the from main the shaft. main The shaft. large The increase large increase in the last in pairthe last of chamberspair of (i.e., 327 chamberschambers (i.e., chambers 8 and 9) was8 and due 9) to was the due ventilation to the ventilation shaft that was shaft connected that was to connected chamber 9to allowing chamber to 9 become 328 allowingfully to filledbecome with fully water. filled For with partially water. aerated For partially chambers, aerated some chambers, of the maximum some of water the maximum 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.

331 332 Figure 7. Maximum differences of water level (WL) in successive chambers of the underground 333 reservoir of the UPSH during (a) turbining and (b) pumping phases for a range of total cross sectional 334 areas, At, of the connecting galleries when the chambers are fully aerated for the winter discharge 335 scenario. Successive chambers are connected with two galleries with roughness height equal to 5 cm.

Energies 2020, 13, x FOR PEER REVIEW 11 of 17

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

320 For partially aerated chambers, the water level differences between adjacent chambers exhibited 321 a more complicated pattern compared to fully aerated chambers. Figure 6 shows that for small 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 monotonicallyEnergies 2020, 13with, 3512 increasing distance from the main shaft. The large increase in the last pair 11of of 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 wateroccurred level differences during equilibrium occurred conditions, during equilibrium thus Figure conditions,6 did not examine thus Figure separately 6 did the not turbining examine and 330 separatelypumping the phases turbining like and Figure pumping7 for the phases fully aeratedlike Figure chambers. 7 for the fully aerated chambers.

331 332 FigureFigure 7. Maximum 7. Maximum differences differences of water of water level level (WL) (WL) in successive in successive chambers chambers of the of theunderground underground 333 reservoirreservoir of the of UPSH the UPSH during during (a) turbining (a) turbining and and(b) pumping (b) pumping phases phases for a for range a range of total of total cross cross sectional sectional 334 areas,areas, At, ofA tthe, of connecting the connecting galleries galleries when when the chambers the chambers are fully are fully aerated aerated for the for winter the winter discharge discharge 335 Energiesscenario. 2020scenario., 13Successive, x FOR Successive PEER chambers REVIEW chambers are connected are connected with with two twogalleries galleries with with roughness roughness height height equal equal to 5 tocm. 5 12 cm. of 17

336 337 FigureFigure 8. 8.MaximumMaximum difference difference of of water water level level (WL) (WL) between between chambers 11 andand9 9 during during ( a()a turbining) turbining and 338 and(b ()b pumping) pumping phases phases for for a rangea range of of total total cross cross sectional sectional areas, areas,A tA,t of, of the the connecting connecting galleries galleries when when the 339 thechambers chambers are are fully fully aerated aerated for for the the winter winter discharge discharge scenario. scenario. Successive Successive chambers chambers are are connected connected with 340 withtwo two galleries galleries with with roughness roughness height height equal equal to 5to cm. 5 cm.

341 TheThe effect effect of ofthe the hydraulic hydraulic roughness roughness of ofthe the co connectingnnecting galleries galleries on on the the water water level level differences differences 342 betweenbetween successive successive chambers chambers was was additionally additionally analyzed. analyzed. So Sofar, far, a 5 a cm 5 cm value value of the of the roughness roughness height, height, 343 ks, kofs, the of the connecting connecting galleries galleries was was considered. considered. An An increase increase of ofks toks to20 20cm cm has has been been examined. examined. The The effect effect 344 of ofincreased increased roughness roughness in inthe the connecting connecting galleries galleries on on maximum maximum water water level level differences differences was was more more 345 prominentprominent for for the the chambers chambers closer closer to tothe the main main shaf shaft,t, both both for for partially partially aerated aerated (Figure (Figure 9)9 and) and fully fully 2 346 aeratedaerated (Figure (Figure 10) 10 chambers.) chambers. The The induced induced differences differences for for a 7 a m 72 m totaltotal cross-sectional cross-sectional area area of ofthe the 347 connectingconnecting galleries galleries exceeded exceeded one one meter meter for for the the first first two two chambers chambers and and became became negligible negligible at atthe the 348 chamberschambers away away from from the the main main shaft. shaft. When When the the tota totall cross cross sectional sectional area area of ofthe the connecting connecting galleries galleries 2 349 increasedincreased from from 7 to 7 to10 10 m2 m, the, the effect effect of ofthe the increasing increasing roughness roughness in inthe the connecting connecting galleries galleries became became 350 muchmuch less less prominent, prominent, especially especially when when the the chambers chambers were were only only partially partially aerated aerated (Figure (Figure 9).9).

351 352 Figure 9. Maximum differences of the water level (WL) in successive chambers of the underground 353 reservoir of the UPSH for different roughness heights, ks, and total cross sectional areas, At, of the 354 connecting galleries when only chamber 9 is aerated for the winter discharge scenario. Successive 355 chambers are connected with two galleries.

Energies 2020, 13, x FOR PEER REVIEW 12 of 17

336 337 Figure 8. Maximum difference of water level (WL) between chambers 1 and 9 during (a) turbining 338 and (b) pumping phases for a range of total cross sectional areas, At, of the connecting galleries when 339 the chambers are fully aerated for the winter discharge scenario. Successive chambers are connected 340 with two galleries with roughness height equal to 5 cm.

341 The effect of the hydraulic roughness of the connecting galleries on the water level differences 342 between successive chambers was additionally analyzed. So far, a 5 cm value of the roughness height, 343 ks, of the connecting galleries was considered. An increase of ks to 20 cm has been examined. The effect 344 of increased roughness in the connecting galleries on maximum water level differences was more 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 FigureFigure 9. 9.MaximumMaximum differences differences of ofthe the water water level level (WL) (WL) in insuccessive successive chambers chambers of ofthe the underground underground 353 reservoirreservoir of ofthe the UPSH UPSH for for different different roughness roughness heights, heights, ks, kands, and total total cross cross sectional sectional areas, areas, At,A oft, ofthe the 354 connectingconnecting galleries galleries when when only only chamber chamber 9 is 9 isaerated aerated for for the the winter winter discharge discharge scenario. scenario. Successive Successive 355 Energieschambers 2020chambers, 13, arex FOR are connected connectedPEER REVIEW with with two two galleries. galleries. 13 of 17

356 357 FigureFigure 10. 10. MaximumMaximum differences differences of ofthe the water water level level (WL) (WL) in insuccessive successive chambers chambers of ofthe the underground underground 358 reservoirreservoir of ofthe the UPSH UPSH during during (a ()a turbining) turbining and and (b (b) )pumping pumping phase phase for for different different roughness heights,heights, ks, 359 ks, andand totaltotal crosscross sectionalsectional areas,areas,A At,t, ofof thethe connectingconnecting galleriesgalleries whenwhen the the chambers chambers are are fully fully aerated aerated for 360 forthe the winter winter discharge discharge scenario. scenario. Successive Successive chambers chambers are are connected connected with with two two galleries. 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 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 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 381 within the first chamber was significantly increased. This reduced the head difference between the 382 upper and lower reservoirs, and decreased the UPSH plant efficiency. To fully exploit the elevation 383 difference between the upper and the lower reservoir, drilling of additional connecting galleries or 384 widening of the existing ones is effective in reducing the water level differences between the 385 chambers. The reduction of water level difference from side to side of (between chambers) pillars will 386 also restrict the exposure to bending forces. However, such works will increase the investment cost 387 and may also weaken the pillars separating the chambers. 388 Another option is to fill the lower reservoir by steps, with breaks in between injections of large 389 portions of water from the upper reservoir, so that the water level becomes uniform across all the 390 interconnected chambers and the hydraulic head in the chamber that is connected to the main shaft 391 is reduced. Such an operating way is however not compatible with the level of flexibility required by 392 energy storage systems. With the operation scenario considered in this study, build upon classical 393 use of an existing pumped storage scheme connected to a grid with a large amount of nuclear and/or 394 production, the results presented above already show prohibitive water elevation 395 variation in the underground reservoir. In a future with much more renewable energy production,

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 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.

References

1. Evans, A.; Strezov, V.; Evans, T.J. Assessment of utility energy storage options for increased renewable energy penetration. Renew. Sustain. Energy Rev. 2012, 16, 4141–4147. [CrossRef] 2. Stram, B.N. Key challenges to expanding renewable energy. 2016, 96, 728–734. [CrossRef] Energies 2020, 13, 3512 15 of 16

3. Rogelj, J.; den Elzen, M.; Höhne, N.; Fransen, T.; Fekete, H.; Winkler, H.; Schaeffer, R.; Sha, F.; Riahi, K.;

Meinshausen, M. Paris Agreement climate proposals need a boost to keep warming well below 2 ◦C. Nature 2016, 534, 631–639. [CrossRef][PubMed] 4. Wilson, I.A.G.; McGregor, P.G.; Hall, P.J. Energy storage in the UK electrical network: Estimation of the scale and review of technology options. Energy Policy 2010, 38, 4099–4106. [CrossRef] 5. Zhang, N.; Lu, X.; McElroy, M.B.; Nielsen, C.P.; Chen, X.; Deng, Y.; Kang, C. Reducing curtailment of wind electricity in by employing electric boilers for and pumped hydro for energy storage. Appl. Energy 2016, 184, 987–994. [CrossRef] 6. Yang, C.-J.; Jackson, R.B. Opportunities and barriers to pumped-hydro energy storage in the . Renew. Sustain. Energy Rev. 2011, 15, 839–844. [CrossRef] 7. Rehman, S.; Al-Hadhrami, L.M.; Alam, M.M. Pumped hydro energy storage system: A technological review. Renew. Sustain. Energy Rev. 2015, 44, 586–598. [CrossRef] 8. Steffen, B. Prospects for pumped-hydro storage in Germany. Energy Policy 2012, 45, 420–429. [CrossRef] 9. Barbour, E.; Wilson, I.A.G.; Radcliffe, J.; Ding, Y.; Li, Y.A review of pumped hydro energy storage development in significant international electricity markets. Renew. Sustain. Energy Rev. 2016, 61, 421–432. [CrossRef] 10. Ming, Z.; Kun, Z.; Daoxin, L. Overall review of pumped-hydro energy storage in China: Status quo, operation mechanism and policy barriers. Renew. Sustain. Energy Rev. 2013, 17, 35–43. [CrossRef] 11. Kucukali, S. Finding the most suitable existing hydropower reservoirs for the development of pumped-storage schemes: An integrated approach. Renew. Sustain. Energy Rev. 2014, 37, 502–508. [CrossRef] 12. Menéndez, J.; Ordóñez, A.; Álvarez, R.; Loredo, J. Energy from closed mines: Underground energy storage and geothermal applications. Renew. Sustain. Energy Rev. 2019, 108, 498–512. [CrossRef] 13. Matos, C.R.; Carneiro, J.F.; Silva, P.P. Overview of large-scale underground energy storage technologies for integration of renewable energies and criteria for reservoir identification. J. Energy Storage 2019, 21, 241–258. [CrossRef] 14. Koohi-Fayegh, S.; Rosen, M.A. A review of energy storage types, applications and recent developments. J. Energy Storage 2020, 27, 101047. [CrossRef] 15. Poulain, A.; de Dreuzy, J.-R.; Goderniaux, P. Pump hydro energy storage systems (PHES) in groundwater flooded quarries. J. Hydrol. 2018, 559, 1002–1012. [CrossRef] 16. Menéndez, J.; Loredo, J.; Galdo, M.; Fernández-Oro, J.M. Energy storage in underground coal mines in NW : Assessment of an underground lower water reservoir and preliminary energy balance. Renew. Energy 2019, 134, 1381–1391. [CrossRef] 17. Winde, F.; Kaiser, F.; Erasmus, E. Exploring the use of deep level gold mines in South for underground pumped hydroelectric energy storage schemes. Renew. Sustain. Energy Rev. 2017, 78, 668–682. [CrossRef] 18. Fan, J.; Xie, H.; Chen, J.; Jiang, D.; Li, C.; Tiedeu, W.N.; Ambre, J. Preliminary feasibility analysis of a hybrid pumped-hydro energy storage system using abandoned coal mine goafs. Appl. Energy 2020, 158, 114007. [CrossRef] 19. Guo, Z.; Ge, S.; Yao, X.; Li, H.; Li, X. cycle sustainability assessment of pumped hydro energy storage. Int. J. Energy Res. 2020, 44, 192–204. [CrossRef] 20. Pujades, E.; Orban, P.; Bodeux, S.; Archambeau, P.; Erpicum, S.; Dassargues, A. Underground pumped storage hydropower plants using open pit mines: How do groundwater exchanges influence the efficiency? Appl. Energy 2017, 190, 135–146. [CrossRef] 21. Pujades, E.; Willems, T.; Bodeux, S.; Orban, P.; Dassargues, A. Underground pumped storage using abandoned works (deep mines or open pits) and the impact on groundwater flow. Hydrogeol. J. 2016, 24, 1531–1546. [CrossRef] 22. Pujades, E.; Jurado, A.; Orban, P.; Ayora, C.; Poulain, A.; Goderniaux, P.; Brouyère, S.; Dassargues, A. Hydrochemical changes induced by underground pumped storage hydropower and their associated impacts. J. Hydrol. 2018, 563, 927–941. [CrossRef] 23. Menéndez, J.; Fernández-Oro, J.M.; Galdo, M.; Loredo, J. Efficiency analysis of underground pumped storage hydropower plants. J. Energy Storage 2020, 28, 101234. [CrossRef] 24. Menéndez, J.; Fernández-Oro, J.M.; Galdo, M.; Loredo, J. Pumped-storage hydropower plants with underground reservoir: Influence of air pressure on the efficiency of the Francis and energy production. Renew. Energy 2019, 143, 1427–1438. [CrossRef] Energies 2020, 13, 3512 16 of 16

25. Pummer, E.; Schüttrumpf, H. Reflection phenomena in underground pumped storage reservoirs. Water 2018, 10, 504. [CrossRef] 26. Erpicum, S.; Archambeau, P.; Dewals, B.; Pirotton, M. Underground pumped hydroelectric energy storage in Wallonia (Belgium) using old mines—Hydraulic modelling of the reservoirs. In Proceedings of the 37th IAHR World Congress, Kuala Lumpur, Malaysia, 14 August 2017; pp. 2984–2991. 27. Menéndez, J.; Fernández-Oro, J.M.; Galdo, M.; Loredo, J. Transient simulation of underground pumped storage hydropower plants operating in pumping mode. Energies 2020, 13, 1781. [CrossRef] 28. Cerfontaine, B.; Charlier, R.; Collin, F.; Taiebat, M. Validation of a new elastoplastic constitutive model dedicated to the cyclic behaviour of brittle rock materials. Rock Mech. Rock Eng. 2017, 50, 2677–2694. [CrossRef] 29. Pujades, E.; Orban, P.; Archambeau, P.; Kitsikoudis, V.; Erpicum, S.; Dassargues, A. Underground pumped-storage hydropower (UPSH) at the Martelange Mine (Belgium): Interactions with groundwater flow. Energies 2020, 13, 2353. [CrossRef] 30. Archambeau, P.; Bodeux, S.; Cerfontaine, B.; Charlier, R.; Dassargues, A.; Erpicum, S.; Frippiat, C.; Goderniaux, P.; Pirotton, M.; Poulain, A.; et al. Smartwater Project—Sites de Stockage Hydraulique—Inventaire,

Analyses Géomécanique, Hydrogéologique et Hydraulique. Convention n◦ 1450316. Report D1.2; Liege University: Liege, Belgium, 2018. (In French) 31. Erpicum, S.; Meile, T.; Dewals, B.J.; Pirotton, M.; Schleiss, A.J. 2D numerical flow modeling in a macro-rough channel. Int. J. Numer. Methods Fluids 2009, 61, 1227–1246. [CrossRef] 32. Qi, L.; Jiang, H. Semismooth karush-kuhn-tucker equations and convergence analysis of newton and quasi-newton methods for solving these equations. Math. Oper. Res. 1997, 22, 301–325. [CrossRef] 33. Machiels, O.; Erpicum, S.; Archambeau, P.; Dewals, B.; Pirotton, M. Theoretical and numerical analysis of the influence of the bottom friction formulation in free surface flow modelling. Water SA 2011, 37, 221–228. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, . This article is an open access article distributed under the terms and conditions of the Creative Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).