**4. Results**

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 9 of 17

to assimilate it to an environment with high degrees of mixing.

## *4.1. Hydraulic Head Fluctuations in the Quarry and Water Exchanges with the Aquifer* Figure 6 shows the simulated hydraulic head variations in the quarry and water exchanges between the quarry and the aquifer as a function of time and pumping–discharge

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

*4.1. Hydraulic Head Fluctuations in the Quarry and Water Exchanges with the Aquifer* 

Figure 6 shows the simulated hydraulic head variations in the quarry and water exchanges between the quarry and the aquifer as a function of time and pumping–discharge operations. Positive and negative values for the exchange flowrate relate to groundwater that flowed towards the quarry and water that flowed from the quarry to the chalk aquifer, respectively. These exchange flow rates were globally inversely correlated to the hydraulic head in the quarry. When the hydraulic head in the quarry increased as a result of a water discharge from the upper reservoir, the exchange rates decreased to negative values, reflecting that water flows from the quarry to the aquifer. The opposite behavior was observed during the pumping phases when the hydraulic head decreased in the quarry. operations. Positive and negative values for the exchange flowrate relate to groundwater that flowed towards the quarry and water that flowed from the quarry to the chalk aquifer, respectively. These exchange flow rates were globally inversely correlated to the hydraulic head in the quarry. When the hydraulic head in the quarry increased as a result of a water discharge from the upper reservoir, the exchange rates decreased to negative values, reflecting that water flows from the quarry to the aquifer. The opposite behavior was observed during the pumping phases when the hydraulic head decreased in the quarry.

**Figure 6.** Hydraulic head variations in the quarry (red line) and flowrate exchange between the quarry and the chalk aquifer (blue line). Positive and negative values for the **Figure 6.** Hydraulic head variations in the quarry (red line) and flowrate exchange between the quarry and the chalk aquifer (blue line). Positive and negative values for the exchange flowrate relate to groundwater that flowed towards the quarry and water that flowed from the quarry to the chalk aquifer, respectively.

exchange flowrate relate to groundwater that flowed towards the quarry and water that flowed from the quarry to the chalk aquifer, respectively. During no-activity phases, exchange rates were positive when the hydraulic head in the quarry was located at a lower elevation than the surrounding piezometric level in the aquifer, and vice-versa. During no-activity phases, the hydraulic head in the quarry continued to vary slightly since water continued to be exchanged between the quarry and the chalk aquifer until an equilibrium was reached. For example, at the end of a pumping During no-activity phases, exchange rates were positive when the hydraulic head in the quarry was located at a lower elevation than the surrounding piezometric level in the aquifer, and vice-versa. During no-activity phases, the hydraulic head in the quarry continued to vary slightly since water continued to be exchanged between the quarry and the chalk aquifer until an equilibrium was reached. For example, at the end of a pumping period, the hydraulic head in the quarry was lower than the surrounding piezometric level in the aquifer. Consequently, the chalk aquifer was drained by the quarry. The exchange rates were positive but decreased slowly, and the hydraulic head in the quarry increased slowly.

period, the hydraulic head in the quarry was lower than the surrounding piezometric level in the aquifer. Consequently, the chalk aquifer was drained by the quarry. The exchange rates were positive but decreased slowly, and the hydraulic head in the quarry In the long term, the average elevation around which the hydraulic head fluctuates tended to be equal to the elevation of the hydraulic head in natural conditions. This fact In the long term, the average elevation around which the hydraulic head fluctuates tended to be equal to the elevation of the hydraulic head in natural conditions. This fact was better observed in the regular scenarios than in the random one because of its more chaotic behavior (Figure 3). This phenomenon of gradual increase in the hydraulic head occurred because the simulated scenarios started with a pumping phase. During this initial phase, the hydraulic head in the quarry fell below the elevation of the hydraulic head in natural conditions. As a result, groundwater inflows from the chalk aquifer to the quarry

was better observed in the regular scenarios than in the random one because of its more

tial phase, the hydraulic head in the quarry fell below the elevation of the hydraulic head

contributed to increase the hydraulic head. This behavior differed to that expected in the case of an isolated lower reservoir where the hydraulic head remained constant and was not influenced by the groundwater exchanges. During discharge phases, when the volume of water previously pumped is discharged into the quarry, the hydraulic head in the quarry increased above its natural elevation, and thus, water was forced to flow from the quarry to the chalk aquifer. However, total water inflows from the aquifer to the quarry were generally greater than losses, as long as the average hydraulic head was below the natural level. Water inflows and outflows were not equilibrated until the hydraulic head oscillated around its natural elevation. This behavior must be considered, especially if there are constraints concerning the maximum hydraulic head to be reached in the quarry such as stability problems related with the elevation of the hydraulic head. Moreover, the gradual increase in the average hydraulic head was also critical because it may affect the balance between energy stored and produced by the system since the efficiency of the pumps and turbines depends on the difference in the hydraulic head between the quarry and the upper reservoir [8].

Table 3 summarizes the results from the simulations regarding the quarry–aquifer exchanges and the hydraulic head fluctuations in the quarry. The amplitude of the hydraulic head fluctuations was about 3 m, despite the large upper reservoir considered. Natural piezometric head fluctuations in the aquifer were 1 to 4 m depending on where you were in the aquifer. Concerning the maximum water exchange rates between the quarry and the chalk aquifer, they reached up to 0.53 m3/s. Slight differences in results were observed for the different pumping–discharge scenarios considered. The maximum variations in the hydraulic head in the requested quarry were less important for the random scenario than for the seasonal scenarios. The difference between them was about 20 cm. This was related with the higher frequency of pumping–discharge cycles of the random scenario since pumped and discharged volumes of water per phase are less important. As a result, fluctuations of the hydraulic head in the quarry as well as the exchange rates with the aquifer were smaller than in the seasonal scenarios. The maximum water exchange rates, which were similar for the three seasonal scenarios, were about 0.5 m3/s, whilst they were about 27% lower for the random scenario.

**Table 3.** Summary of the results concerning the quarry–groundwater interactions and hydraulic head fluctuations in the quarry during the simulations. These data concern the minimum and maximum hydraulic head in the quarry, the maximum variation in the hydraulic head in the quarry, and the maximum exchange flowrate between the quarry and the aquifer for each scenario.

