3.1.4. Simulated Pump–Storage Operations Scenarios

Four pumping–discharge scenarios (Figure 4) have been considered (Smartwater project, 2018; [4,7]). The pumping–discharge scenarios, which were implemented as boundary conditions in the models, are based on real electricity data. These scenarios describe the emptying and filling of the upper reservoir and the alternating phases of pumping, discharge, and no-activity over a period of fourteen days. In Figure 3, negative flow rate values correspond to pumping operations in the quarry and filling of the upper reservoir. Positive flow rate values correspond to discharge steps of the upper reservoir through the turbines and injection in the quarry. Three of the pumping–discharge scenarios are based on the electricity market daily data at different seasons of the year (spring, summer, and winter). The pumping and discharge periods take approximately five hours. The succession of the different phases (pumping/discharge/no-activity) is faster in winter, intermediate in spring, and slower in summer. The last scenario was generated randomly, with a change of phase (i.e., pumping/discharge/no-activity) every 15 min, following a uniform law. This scenario has been developed in line with PSH stations potentially connected to renewable and intermittent energy sources, whose production management would probably require higher frequencies, with periods shorter than an hour. The pumping–discharge scenarios were used as input data for the numerical model and were implemented by prescribing the flow rates (i.e., Neuman boundary conditions) in the cells corresponding to the quarry. The pumping and discharge flow rates were chosen according to the volume of the upper reservoir (≈1 million m<sup>3</sup> ) to satisfy that it can be filled or emptied during one pumping/discharge cycle. Thus, for an example cycle of 4.8 h, the pumping/discharge rate was 55.56 m3/s.

pumping/discharge rate was 55.56 m³/s.

would probably require higher frequencies, with periods shorter than an hour. The pumping–discharge scenarios were used as input data for the numerical model and were implemented by prescribing the flow rates (i.e., Neuman boundary conditions) in the cells corresponding to the quarry. The pumping and discharge flow rates were chosen according to the volume of the upper reservoir (≈1 million m³) to satisfy that it can be filled or

**Figure 4.** Pumping-discharge scenarios developed and used as inputs to the numerical flow model. Negative flow rate values correspond to pumping operations in the quarry **Figure 4.** Pumping-discharge scenarios developed and used as inputs to the numerical flow model. Negative flow rate values correspond to pumping operations in the quarry and filling of the upper reservoir. Positive flow rate values correspond to discharge steps of the upper reservoir through the turbines and injection in the quarry.

## and filling of the upper reservoir. Positive flow rate values correspond to discharge steps *3.2. Groundwater Hydrochemical Model*

### of the upper reservoir through the turbines and injection in the quarry. 3.2.1. Conceptual Model

*3.2. Groundwater Hydrochemical Model*  3.2.1. Conceptual Model To simulate the hydrochemical evolution of the water contained in the upper reservoir, in the quarry, and in the chalk aquifer (Figure 5), several hypotheses were established concerning the aquifer and the hydrochemical characteristics of the groundwater and the pump–storage operations. The porous medium was considered as homogeneous. The hydraulic conductivity and the drainage porosity were identical at each point of the rock media. Values were identical to those used for the flow groundwater model described in Section 3.1. The rock was considered to be composed of 92% calcite, reflecting the composition of the chalk of the Trivières geological formation. The pumping and discharge flowrates were derived from the pumping–storage scenarios described in the groundwater flow model and consisting of regular successive pumping and discharge slots, the period of which was 4.8 h for 14.6 days. The volume of pumped and then discharged water during each cycle was 125,000 m³. It is considered that chemical equilibrium with the atmosphere was reached in the upper reservoir before each discharge phase assuming partial pressures for O2 and CO2 of 10−0.7 bar and 10−3.5 bar, respectively. In the initial state, the water present in the quarry was considered to be in equilibrium with the groundwater in To simulate the hydrochemical evolution of the water contained in the upper reservoir, in the quarry, and in the chalk aquifer (Figure 5), several hypotheses were established concerning the aquifer and the hydrochemical characteristics of the groundwater and the pump–storage operations. The porous medium was considered as homogeneous. The hydraulic conductivity and the drainage porosity were identical at each point of the rock media. Values were identical to those used for the flow groundwater model described in Section 3.1. The rock was considered to be composed of 92% calcite, reflecting the composition of the chalk of the Trivières geological formation. The pumping and discharge flowrates were derived from the pumping–storage scenarios described in the groundwater flow model and consisting of regular successive pumping and discharge slots, the period of which was 4.8 h for 14.6 days. The volume of pumped and then discharged water during each cycle was 125,000 m<sup>3</sup> . It is considered that chemical equilibrium with the atmosphere was reached in the upper reservoir before each discharge phase assuming partial pressures for O<sup>2</sup> and CO<sup>2</sup> of 10−0.7 bar and 10−3.5 bar, respectively. In the initial state, the water present in the quarry was considered to be in equilibrium with the groundwater in the aquifer. In the quarry, the equilibrium of the first few meters of water with the atmosphere was neglected. The temperature and density of the water were considered to be constant and equal to 12 ◦C and 1000 Kg/m<sup>3</sup> , respectively. Despite variations in water temperature and density, which were expected to be negligible within the quarry, further investigations by using numerical codes with more capabilities should be developed to establish their role in the system's behavior. The used numerical code does not allow temperature variation within the same simulation.

the aquifer. In the quarry, the equilibrium of the first few meters of water with the atmosphere was neglected. The temperature and density of the water were considered to be constant and equal to 12 °C and 1000 Kg/m3, respectively. Despite variations in water temperature and density, which were expected to be negligible within the quarry, further intions.

tablish their role in the system's behavior. The used numerical code does not allow tem-

perature variation within the same simulation.

**Figure 5.** Schematization of the hydrogeochemical model. **Figure 5.** Schematization of the hydrogeochemical model.

### 3.2.2. Numerical Model and Boundary Conditions 3.2.2. Numerical Model and Boundary Conditions

The model was three-dimensional and was developed using the finite difference code PHAST [28]. PHAST aims to simulate groundwater flow, solute transport, and the hydrogeochemical reactions. PHAST couples HST3D [29], which computes flow and solute transport processes, with PHREEQC [30], which simulates the hydrogeochemical reac-The model was three-dimensional and was developed using the finite difference code PHAST [28]. PHAST aims to simulate groundwater flow, solute transport, and the hydrogeochemical reactions. PHAST couples HST3D [29], which computes flow and solute transport processes, with PHREEQC [30], which simulates the hydrogeochemical reactions.

Taking advantage of the symmetry of the problem, only one quarter of the system was modeled, allowing a significant reduction in computation time. As for the groundwater flow model, the 2-km long domain was discretized with irregular rectangular cells. The size of the cells was 10 m × 10 m in the quarry and increased progressively by a factor of 1.05 towards the boundaries. The piezometric head was prescribed (Dirichlet BCs) at the outer boundaries of the model. The size of the modelled zone was chosen so that these limits were sufficiently far from the quarry to not influence the effects of pumping–discharge operations. This choice was based on the results of the groundwater flow model developed (Section 3.1). Note that the prescribed head at the outer boundaries was uniform, and thus, the regional piezometric gradient was not represented. The pumping and discharge flows were simulated by implementing a Neumann BC in the center of the quarry. The hydrochemical characteristics of the water released into the quarry during the discharge phases depended on the results of the routine relating to the upper reservoir Taking advantage of the symmetry of the problem, only one quarter of the system was modeled, allowing a significant reduction in computation time. As for the groundwater flow model, the 2-km long domain was discretized with irregular rectangular cells. The size of the cells was 10 m × 10 m in the quarry and increased progressively by a factor of 1.05 towards the boundaries. The piezometric head was prescribed (Dirichlet BCs) at the outer boundaries of the model. The size of the modelled zone was chosen so that these limits were sufficiently far from the quarry to not influence the effects of pumping–discharge operations. This choice was based on the results of the groundwater flow model developed (Section 3.1). Note that the prescribed head at the outer boundaries was uniform, and thus, the regional piezometric gradient was not represented. The pumping and discharge flows were simulated by implementing a Neumann BC in the center of the quarry. The hydrochemical characteristics of the water released into the quarry during the discharge phases depended on the results of the routine relating to the upper reservoir and were readapted to each new pump–discharge cycle.

### and were readapted to each new pump–discharge cycle. 3.2.3. Parameterization

3.2.3. Parameterization The quarry was assimilated as a linear reservoir with a high hydraulic conductivity and a porosity of 100%. Hydraulic conductivity and drainage porosity values assigned to the elements representing the chalk aquifer were the same as those implemented in the groundwater flow model (Section 3.1) and were equal to 10−5 m·s−1 and 0.16, respectively. In this case, we considered the total porosity because the groundwater exchanges and the potential environmental impacts increased with high porosities [7,31]. Concerning the solute transport parameters, the longitudinal and transverse dispersivities were 10 m and 1 The quarry was assimilated as a linear reservoir with a high hydraulic conductivity and a porosity of 100%. Hydraulic conductivity and drainage porosity values assigned to the elements representing the chalk aquifer were the same as those implemented in the groundwater flow model (Section 3.1) and were equal to 10−<sup>5</sup> <sup>m</sup>·<sup>s</sup> <sup>−</sup><sup>1</sup> and 0.16, respectively. In this case, we considered the total porosity because the groundwater exchanges and the potential environmental impacts increased with high porosities [7,31]. Concerning the solute transport parameters, the longitudinal and transverse dispersivities were 10 m and 1 m, respectively, and the tortuosity was equal to 1. The longitudinal and transverse dispersivities adopted to simulate the water behavior in the quarry were equal to 100 m in order to assimilate it to an environment with high degrees of mixing.

**4. Results** 

increased slowly.
