*4.2. Piezometric Head Fluctuations in the Aquifer*

Figure 7 shows the zone of influence of pumping–discharge operations at the end of the simulations (after 14 days) for all simulated scenarios.

**Figure 7.** Zone of influence of pumping–discharge operations around the Obourg quarry at the end of the simulation time (14 days). A threshold of 0.1 m for piezometric head variations was **Figure 7.** Zone of influence of pumping–discharge operations around the Obourg quarry at the end of the simulation time (14 days). A threshold of 0.1 m for piezometric head variations was assumed to delimitate the area of influence. If piezometric head fluctuations were lower than this threshold, it was considered as outside the zone of influence of PSH operations in the aquifer.

assumed to delimitate the area of influence. If piezometric head fluctuations were lower than this

threshold, it was considered as outside the zone of influence of PSH operations in the aquifer. This zone of influence corresponds to an area in which the fluctuations of the piezometric head were larger than 0.1 m. The typical summer, winter, and spring scenarios were a priori considered as low frequency scenarios in comparison with the random scenario, and thus, greater distances of influence were expected. However, the maximum distance of influence was similar in all scenarios. For all of them, the induced variations of the piezometric head (Δ*h*) were less than 0.1 m within a maximum distance of 380 m around the quarry walls. This similarity between scenarios is probably explained by the fact that the pumping–discharge scenarios were not sinusoidal and mono-frequent but contained several frequencies. This effect is particularly visible on the hydraulic head fluc-This zone of influence corresponds to an area in which the fluctuations of the piezometric head were larger than 0.1 m. The typical summer, winter, and spring scenarios were a priori considered as low frequency scenarios in comparison with the random scenario, and thus, greater distances of influence were expected. However, the maximum distance of influence was similar in all scenarios. For all of them, the induced variations of the piezometric head (∆*h*) were less than 0.1 m within a maximum distance of 380 m around the quarry walls. This similarity between scenarios is probably explained by the fact that the pumping–discharge scenarios were not sinusoidal and mono-frequent but contained several frequencies. This effect is particularly visible on the hydraulic head fluctuations in the quarry simulated for the random scenario (Figure 4). The lower frequencies control the distance of influence [7]. In addition, the presence of large water bodies around the quarry limited the extension of the zone of influence. In other words, the quarries located at both sides of the central Obourg quarry act as a kind of buffer.

tuations in the quarry simulated for the random scenario (Figure 4). The lower frequencies control the distance of influence [7]. In addition, the presence of large water bodies around the quarry limited the extension of the zone of influence. In other words, the quarries located at both sides of the central Obourg quarry act as a kind of buffer. The results reflect the importance of considering these interactions to maximize the efficiency and to minimize the potential environmental impacts. Results obtained with the groundwater flow model show the preponderant influence of the lower frequency of the The results reflect the importance of considering these interactions to maximize the efficiency and to minimize the potential environmental impacts. Results obtained with the groundwater flow model show the preponderant influence of the lower frequency of the pumping–discharge cycles. The lower the frequency, and thus the longer the pumping– discharge cycles, the greater the quarry–aquifer interactions. Realistic pumping–discharge scenarios (winter, spring, and summer) used as input to the models had a minimum period of 5 h. If PSH stations are connected to renewable and intermittent energy sources, the management of this production would probably require higher frequencies, with periods shorter than an hour. The random scenario was developed accordingly. Concerning the

tion of the safety side and the potentially largest zones of influence [7].

pumping–discharge cycles. The lower the frequency, and thus the longer the pumping–

mum period of 5 h. If PSH stations are connected to renewable and intermittent energy sources, the management of this production would probably require higher frequencies, with periods shorter than an hour. The random scenario was developed accordingly. Concerning the distances of influence, however, studying low frequencies allows consideradistances of influence, however, studying low frequencies allows consideration of the safety side and the potentially largest zones of influence [7].

### *4.3. Evolution of Water Chemistry in the Upper Reservoir 4.3. Evolution of Water Chemistry in the Upper Reservoir*

the evolution of pH and the precipitated quantities of calcite, pyrolusite, and goethite.

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 12 of 17

The following results are related to the hydrochemical context described at 2.3. Figure 8 shows the main results simulated with the hydrochemical groundwater model concerning the hydrochemical evolution of the water in the upper reservoir. Figure 7 displays the evolution of pH and the precipitated quantities of calcite, pyrolusite, and goethite. The following results are related to the hydrochemical context described at 2.3. Figure 8 shows the main results simulated with the hydrochemical groundwater model concerning the hydrochemical evolution of the water in the upper reservoir. Figure 7 displays

**Figure 8.** Evolution of hydrogeochemical variables during pumping–injection cycles in the quarry. (**a**) Evolution of pH. (**b**) Evolution of the quantity of Ca2+ in moles per liter. (**c**) Evolution of the quantity of Mn2+ in moles per liter. (**d**) Evolution of the quantity of Fe2+ in moles per liter. **Figure 8.** Evolution of hydrogeochemical variables during pumping–injection cycles in the quarry. (**a**) Evolution of pH. (**b**) Evolution of the quantity of Ca2+ in moles per liter. (**c**) Evolution of the quantity of Mn2+ in moles per liter. (**d**) Evolution of the quantity of Fe2+ in moles per liter.

In the upper reservoir, the chemical equilibrium of the water with the atmosphere induced an increase in the concentration of dissolved O2 and a decrease in the concentration of dissolved CO2. In general, the increase in the dissolved O2 caused the precipitation of pyrolusite and goethite (Equations 6 and 7), whereas the decrease in dissolved CO2 caused the precipitation of calcite (Equations 1 to 5). The precipitation of these elements occurred from the first pumping–discharge cycle, during which the amount of precipitated minerals reached a maximum (1.46 × 10−6, 4.55 × 10−6, and 1.4×10−3 moles of precipitate/L of pyrolusite, goethite, and calcite, respectively) as shown in [9] in the scenario with only calcite. Precipitation continued during the following cycles, but the amount of precipitated minerals decreased gradually as the water pumped into the upper reservoir became depleted in calcium, manganese, and iron. The precipitated quantities were significant, especially at the beginning of the PSH activities. The quantity of precipitated calcite was three orders of magnitude higher than those of goethite and pyrolusite. Precipitated amounts of goethite and pyrolusite were similar, although slightly higher for goethite. Indeed, the iron concentration (4.7 × 10−6 mol/L) in groundwater was initially higher than that of manganese (1.5 × 10−6 mol/L). In addition, iron oxidation is preferential and has In the upper reservoir, the chemical equilibrium of the water with the atmosphere induced an increase in the concentration of dissolved O<sup>2</sup> and a decrease in the concentration of dissolved CO2. In general, the increase in the dissolved O<sup>2</sup> caused the precipitation of pyrolusite and goethite (Equations (6) and (7)), whereas the decrease in dissolved CO<sup>2</sup> caused the precipitation of calcite (Equations (1) to (5)). The precipitation of these elements occurred from the first pumping–discharge cycle, during which the amount of precipitated minerals reached a maximum (1.46 <sup>×</sup> <sup>10</sup>−<sup>6</sup> , 4.55 <sup>×</sup> <sup>10</sup>−<sup>6</sup> , and 1.4×10−<sup>3</sup> moles of precipitate/L of pyrolusite, goethite, and calcite, respectively) as shown in [9] in the scenario with only calcite. Precipitation continued during the following cycles, but the amount of precipitated minerals decreased gradually as the water pumped into the upper reservoir became depleted in calcium, manganese, and iron. The precipitated quantities were significant, especially at the beginning of the PSH activities. The quantity of precipitated calcite was three orders of magnitude higher than those of goethite and pyrolusite. Precipitated amounts of goethite and pyrolusite were similar, although slightly higher for goethite. Indeed, the iron concentration (4.7 <sup>×</sup> <sup>10</sup>−<sup>6</sup> mol/L) in groundwater was initially higher than that of manganese (1.5 <sup>×</sup> <sup>10</sup>−<sup>6</sup> mol/L). In addition, iron oxidation is preferential and has faster kinetics. Theoretically, calcite, pyrolusite, and goethite should form deposits in the upper reservoir, which would require periodic cleaning tasks. In practice, however, given the flows involved, turbulence in the upper reservoir could reduce these deposits. Overall, the volume of precipitated minerals can be relatively important

the volume of precipitated minerals can be relatively important and periodical cleaning tasks could be needed, which would affect the global efficiency of the PSH plant [9,32]

with calcite precipitation, and potentially needed cleaning operations.

*4.4. Hydrochemical Evolution of the Water in the Quarry* 

pH values in the upper reservoir increased drastically during the first pumping–discharge cycle as a result of CO2 degassing and calcite precipitation. After the first cycle, pH remained relatively constant throughout the following cycles, oscillating between 8.16 and 8.18. Note that incrustations were promoted under these values of pH, in accordance ervoir).

(Figure 10).

and periodical cleaning tasks could be needed, which would affect the global efficiency of the PSH plant [9,32] charge cycles, whereas the average pH increases (Figure 9). The evolution of pH in the quarry was related to that in the upper reservoir where the pH increased abruptly during

Concentrations of Ca2+, Fe2+, and Mg2+ tend to decrease during the pumping–dis-

pH values in the upper reservoir increased drastically during the first pumping– discharge cycle as a result of CO<sup>2</sup> degassing and calcite precipitation. After the first cycle, pH remained relatively constant throughout the following cycles, oscillating between 8.16 and 8.18. Note that incrustations were promoted under these values of pH, in accordance with calcite precipitation, and potentially needed cleaning operations. the first cycle. During discharge phases, the pH of the released water was higher than that of the water in the quarry, and thus, the pH in the quarry tended to increase during each discharge phase. Conversely, during the pumping periods, water from the chalk aquifer, which had lower values of pH than that in the quarry and upper reservoir, inflowed to the quarry causing its pH to decrease. Overall, the pH of the water in the quarry gradually

### *4.4. Hydrochemical Evolution of the Water in the Quarry* increased towards an average value between the pH of the aquifer and the pH of the up-

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 13 of 17

Concentrations of Ca2+, Fe2+, and Mg2+ tend to decrease during the pumping–discharge cycles, whereas the average pH increases (Figure 9). The evolution of pH in the quarry was related to that in the upper reservoir where the pH increased abruptly during the first cycle. During discharge phases, the pH of the released water was higher than that of the water in the quarry, and thus, the pH in the quarry tended to increase during each discharge phase. Conversely, during the pumping periods, water from the chalk aquifer, which had lower values of pH than that in the quarry and upper reservoir, inflowed to the quarry causing its pH to decrease. Overall, the pH of the water in the quarry gradually increased towards an average value between the pH of the aquifer and the pH of the upper reservoir through cumulative effects [33]. The volumes of groundwater and chalk rock present in the surrounding aquifer stabilized the chemical equilibrium of the groundwater. This also explains the pH evolution in the quarry towards intermediate values compared to the upper reservoir. per reservoir through cumulative effects [33]. The volumes of groundwater and chalk rock present in the surrounding aquifer stabilized the chemical equilibrium of the groundwater. This also explains the pH evolution in the quarry towards intermediate values compared to the upper reservoir. The opposite behavior was observed for Ca2+, Fe2+, and Mg2+. In this case, as a result of calcite, pyrolusite, and goethite precipitation, their concentrations were lower in the upper reservoir than in the chalk aquifer. Thus, concentrations of Ca2+, Fe2+, and Mg2+ increase during pumping phases (water flows from the aquifer towards the lower reservoir) and decrease during discharge phases (the quarry is filled with water from the upper res-

**Figure 9.** Evolution of hydrogeochemical variables during pumping–injection cycles in the quarry. (**a**) Evolution of pH. (**b**) Evolution of the quantity of Ca2+ in moles per liter. (**c**) Evolution of the **Figure 9.** Evolution of hydrogeochemical variables during pumping–injection cycles in the quarry. (**a**) Evolution of pH. (**b**) Evolution of the quantity of Ca2+ in moles per liter. (**c**) Evolution of the quantity of Mn2+ in moles per liter. (**d**) Evolution of the quantity of Fe2+ in moles per liter.

quantity of Mn2+ in moles per liter. (**d**) Evolution of the quantity of Fe2+ in moles per liter. *4.5. Hydrochemical Evolution of the Groundwater in the Chalk Aquifer*  Regarding the hydrochemical evolution in the aquifer, pH values tended to increase, as in the quarry, but only within a zone limited to the first 20 meters around the quarry The opposite behavior was observed for Ca2+, Fe2+, and Mg2+. In this case, as a result of calcite, pyrolusite, and goethite precipitation, their concentrations were lower in the upper reservoir than in the chalk aquifer. Thus, concentrations of Ca2+, Fe2+, and Mg2+ increase during pumping phases (water flows from the aquifer towards the lower reservoir) and decrease during discharge phases (the quarry is filled with water from the upper reservoir).

### *4.5. Hydrochemical Evolution of the Groundwater in the Chalk Aquifer Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 14 of 17

Regarding the hydrochemical evolution in the aquifer, pH values tended to increase, as in the quarry, but only within a zone limited to the first 20 meters around the quarry (Figure 10).

**Figure 10.** pH evolution in the quarry and at 10, 20, and 50 m around the quarry. **Figure 10.** pH evolution in the quarry and at 10, 20, and 50 m around the quarry.

The increase was lower than in the quarry because of the quantity of water present in the aquifer and the buffering effect of the chalk rock. In addition, the propagation of hydrochemical stresses induced by the pumping–discharge cycles did not lead to the dissolution of calcite within the chalk aquifer since the acidification phenomenon was not The increase was lower than in the quarry because of the quantity of water present in the aquifer and the buffering effect of the chalk rock. In addition, the propagation of hydrochemical stresses induced by the pumping–discharge cycles did not lead to the dissolution of calcite within the chalk aquifer since the acidification phenomenon was not intensive enough.
