Underground Pumped-Storage Hydropower (UPSH) at the Martelange Mine (Belgium): Interactions with Groundwater Flow
Abstract
:1. Introduction
2. Materials and Methods
2.1. Problem Statement
2.2. Numerical Model
2.2.1. Code
2.2.2. Model Characteristics
- Underground reservoir: The underground reservoir consists of nine underground chambers (CH1 to CH9) linked by galleries located at their bottoms. Each pair of contiguous chambers are linked with one gallery. In addition, a rectangular prism, which links the underground reservoir to the surface, is added adjacent to the CH1 (Figure 2 and Figure 3) to conceptually represent the shaft through which water is pumped and discharged (from now called operation shaft).
- Model dimensions: The modeled domain consists in a square with a side of 2200 m and a height of 180 m (Figure 2 and Figure 3). The chambers (i.e., the underground reservoir) are located in the middle of the domain, approximately, at a distance of 1000 m from the external boundaries of the model. This distance is enough to minimize the influence of the external boundaries on the groundwater dynamics around the underground reservoir.
- Spatial discretization: The mesh is made up of prismatic 3D elements and is divided vertically in 29 layers. The horizontal size of the elements decreases towards the underground reservoir (from 150 m near the external boundaries to 5 m in the center of the domain) (Figure 3). The number of elements and nodes is 64,844 and 38,680, respectively.
- Temporal discretization: The simulation period covers one year and the simulation time step is 15 min. Induced piezometric head oscillations are relatively large and convergence problems arise in the limit between the saturated and unsaturated zone if time steps are larger than 15 min.
- Hydraulic parameters: The hydraulic parameters used in the model are typical of slate mines and are representative of the known underground properties at the considered mine site [44,45]. The hydraulic conductivity is 10−7 m/s, the specific storage coefficient is 10−4 m−1, the saturated water content is 0.05 and the residual water content is 0.01.
- Boundary conditions (BCs): Pumping from and discharge into the underground reservoir are simulated by prescribing the flow at the bottom of the operation shaft (Neuman BC). An internal dynamic Fourier BC, which is head-dependent [35], is implemented to simulate the groundwater exchanges between the underground reservoir (chambers and operation shaft) and the surrounding medium. Regarding the external boundaries, the piezometric head is prescribed (Dirichlet BC) at an elevation with respect the bottom of the model of 121 and 120 m on the upgradient (W) and downgradient (E) sides, respectively. As a result, the underground reservoir is practically flooded (saturated) in natural conditions and groundwater flows from W to E with a hydraulic gradient of 4.6·10−4. The boundary conditions adopted at the external boundaries are maintained constant through the simulations. This fact is a simplification since the piezometric head at the Martelange site oscillates slightly seasonally [46]. However, seasonal oscillations are small enough to not alter the results noticeably. Finally, no-flow BCs are adopted at the top and the bottom of the model and at the N and S boundaries.
- Modeling approach: The domain, except the linear reservoir, is modeled as a porous medium, thus the fractured medium is replaced by an Equivalent Porous Medium (EPM) approach. Although the EPM approach does not allow modelling individual fractures [47] it is suitable for estimating the global behaviour of such a system and computing the main trends. Several studies have demonstrated the efficiency of the EPM approach for modelling fractured aquifers, among others, [48,49]. In addition, the presence of multiple fractures in the study site induces the continuity of the groundwater behavior like in a porous medium.
2.2.3. Initial Conditions—Scenarios
2.2.4. Operation Scenario
- Two realistic constraints were adopted. These consisted of (1) establishing the duration of pumping and discharge phases to 5 h, and (2) assuming that the usable volume of the underground reservoir is completely emptied and filled once a day. Therefore, there are 14 h per day during in which no operations are carried out and the system is in the same condition at the beginning of every day (underground reservoir filled at maximum).
- Frequencies were defined on an hourly basis to maximize economic benefit of the plant operation, i.e., to maximize the balance between electricity cost during pumping and money income when discharging. Every hour, a choice was made between three possibilities (pumping, discharge or no-operation) in order to get at the end of the day 5 h of pumping, then 5 h of discharge and 14 h of no-operation. Pumping, discharge or no-operation hours are not necessary consecutive. For each day, the cheapest 5 h are selected for pumping, and the most expensive 5 h for discharge.
- The underground reservoir is filled faster than when water exchanges are neglected, and therefore, water cannot be discharged despite it is required given the defined pumping–discharge frequency.
- The underground reservoir is emptied faster than when water exchanges are neglected. In this case, water cannot be pumped despite it is required by the defined pumping–discharge frequency. In the modeled case, this situation only arises at the beginning of the scenario E-CI when an initial pumping is not allowed because the underground reservoir is totally filled. During the rest of the simulations, this situation never arises again since inflows of water from the surrounding medium into the underground reservoir are always higher than outflow.
3. Results and Discussion
3.1. Piezometric Head Evolution
3.2. Hydraulic Head Evolution
3.3. Water Exchanges
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Location | Upgradient | Downgradient | ||
---|---|---|---|---|
Distance from the reservoir | 5 m | 15 m | 5 m | 15 m |
Winter | 17.82 m | 3 m | 18.7 m | 5 m |
Spring/Autumn | 17.2 m | 3 m | 19.2 m | 6 m |
Summer | 18.27 m | 4 m | 29.3 m | 8 m |
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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. https://doi.org/10.3390/en13092353
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(9):2353. https://doi.org/10.3390/en13092353
Chicago/Turabian StylePujades, Estanislao, Philippe Orban, Pierre Archambeau, Vasileios Kitsikoudis, Sebastien Erpicum, and Alain Dassargues. 2020. "Underground Pumped-Storage Hydropower (UPSH) at the Martelange Mine (Belgium): Interactions with Groundwater Flow" Energies 13, no. 9: 2353. https://doi.org/10.3390/en13092353