Descriptive statistics
The basic statistics of the groundwater parameters of El Hamma geothermal reservoir are presented in Table 1. The standard deviation values are lower than the average values for all elements. Knowing that the standard deviation makes it possible to measure the dispersion of values around the average, in this specific case the values of the standard deviation are lower; This indicates that the values of the variables are scattered. Thus, it highlights a certain heterogeneity of the water extracted from the aquifer in the study area.
Table 1
| Average | Standard. Deviation | Variance | Skewness | Kurtosis | Minimum | Maximum |
TEMPERATURE | 41.515 | 13.773 | 189,700 | 0.016 | -1.181 | 18.617 | 65.496 |
PZ | 55.101 | 10.802 | 116.686 | -0.503 | 0.047 | 25.924 | 76.529 |
ELEV | 67.621 | 8.416 | 70.825 | 0.861 | 0.913 | 51.019 | 98,000 |
Piezometric Of The Shallow Geothermal Aquifer Of El Hamma
The shallow aquifer of El Hamma knew in the last decades an increase of exploitation. This evolution varies according to a straight line of the form y = 0.4368 x – 863.01 (Fig. 4) Which generates an increase of 4.368 Mm3 between 2002 and 2021.
On an annual scale, the piezometric level of the shallow aquifer of El Hamma has recorded a continuous decline, due to the incessant increase in exploitation and limited recharge. The value of the average annual drop in this water table is generally between − 0.4 m/year and − 3 m/year during dry years.
Current piezometric of the shallow aquifer.
The piezometric level analysis of the shallow geothermal aquifer of El Hamma is based on the database of the 130 monitored water points where the piezometric level could be measured. In the study area, the piezometric level varies from 25.9 to 76.5 m with a low asymmetry coefficient of the order of -0.503, which suggests that the piezometric data follow a normal distribution. The kurtosis coefficient (Kurtosis is 0.047) which indicates a homogeneous series of piezometric data.
In order to represent the spatial distribution of the piezometry of the shallow geothermal aquifer from field measurements, the geostatic technique was used to reduce the interpolation uncertainty at an unsampled location. this technique is based on variographic analysis (Agoubi et al. 2015)
The variographic analysis of the piezometric levels of the hydrothermal waters of the region of El Hamma was developed by the Surfer software. The most appropriate model in this area is the power model (Fig. 5 and Table 2). This model was validated by cross-validation between the observed and expected values by the piezometric level model, illustrated in Fig. 6. There is a very good match between the data observed and estimated by the model, which confirms the choice of a power model is well suited to modeling the spatial variation of the piezometric level of the hydrothermal aquifer. The RMSE is also used to test the performance of the model. This parameter is often used to compare the performance of interpolation methods. The value of the RMSE is 2.928.
Table 2
Variographic parameters for the piezometric leve
Model
|
Variogram component
|
Anisotropy
|
Cross-validation
|
Lag size
|
Portal Sill
|
Tidy
|
Power
|
Ratio
|
Angle
|
RMSE
|
Power
|
524.4458467
|
0.01243
|
1
|
1.173
|
1.272
|
35.43
|
2.9287
|
The piezometric map of El Hamma aquifer (Fig. 7) created for 2021 shows two overall directions of flow, the first in the direction southeast northwest of Jebal Ragouba towards the depression of Sebkhat El Hamma. The second direction is from Mount Aziza west to Wadi El Hamma and the Sebkha depression, and also from Jebal Ragouba to the plain of Jeffara to the east. These results confirm the results of previous studies, especially Abidi 2004 and Agoubi 2018.
Thermal Modeling
Coupled hydrodynamic/thermal numerical modeling has been used by several authors such as: Le Fanic (2005); Thiebaud (2008); Sonney et al. (2012); TOTH et al. (2017) and C. Wang et al. (2021) on one hand to understand the functioning of thermal systems and on the other hand for the numerical validation of hypotheses of circulation of deep and superficial geothermal groundwater. A hydrodynamic/thermal model is applied to the geothermal aquifer systems of El Hamma based on the spatial temperature distribution of groundwater.
The temperature of the hydrothermal waters of the shallow aquifer are quite heterogeneous and they vary between 18.5 to 65.5°C, with an average of 41.5°C,
The variographic analysis shows that the temperature is modeled by a power model (Fig. 8 and Table 3). In order to assess the performance of the model, cross-validation is used. This model is validated by a significant correlation between the estimated values and those measured (Fig. 8). The average square error is 5.9, which suggests the quality of prediction. We notice a very good match between the observed and estimated data which confirms the choice of this model is suitable for modeling the spatial variability of groundwater temperature by the Kriging technique.
Table 3
Variographic model parameters of groundwater temperatur
Model
|
Variogram component
|
Anisotropy
|
Cross-validation
|
Lag size
|
Portal Sill
|
Range
|
Power
|
Ratio
|
Angle
|
RMSE
|
Power
|
531.2005231
|
2.426
|
1
|
0.4896
|
1.583
|
2.587
|
5.908
|
The spatial distribution map of shallow groundwater temperature in the study area (Fig. 9) shows a very heterogeneous distribution. In general, temperature values decrease with groundwater flow directions. It decreases from 60°C from Jebel Aziza (southwest) next to the F1 fault to 15°C in the Sebkhet El Hamma depression in the northeast and also decreases from 65°C in the middle of the Jebal basin Ragouba in the south (fault F5) towards the north of the study area (18°C). Similarly, at Chanchou, the eastern part of the study area, the temperature decreases by 63.5°C from the axis of the F7 fault towards the plain of Jeffara where the temperature is 20°C.
The graph of water temperature against the X direction of Jebel Aziza at Chanchou (Fig. 10) shows temperature fluctuation with the direction of water flow from the western part to the eastern part of the study area, where the temperature of shallow groundwater increases as we approach the axis of the faults located in the area where the water temperature near the F1 fault is 61 degrees, while in the fault F5, it is 65 degrees. In the areas between the fault the temperature decreases to reach 20 degrees.
The temperature profile according to the water sample along the axis fault F5 (from Jebel Ragouba to Sebkhet El Hamma in Fig. 11) shows a decrease in temperature from the southern part (Jebel Ragouba) where the water temperature reaches about 65°C to the northern part from the study region (20°C). The direction of water cooling is not linear. It shows an equivalent aspect that indicates slow cooling due to the aerodynamic effect (Agoubi 2018).
The high-water temperatures observed in El Hamma’s surficial aquifer is a tracer of groundwater flow (Agoubi 2018, Luijendijk et al., 2020, Salem et al. 2020, Agoubi 2021) indicating a flow hot water from the deep Continental Intercalary aquifer. (Abidi 2004; Agoubi et al. 2015) to the SI superficial aquifer through localized fault networks in the region mainly F1, F2, F5 and F7. Indeed, the water temperature in the CI aquifer is about 78°C.
A synthetic vertical section of west to east direction of the temperature distribution of a geothermal aquifer of El Hamma was carried out (Fig. 12 and Fig. 13). Groundwater temperature increases with depth due to the geothermal gradient which in the study area is 0.45°C/km (Agoubi et al. 2018). However, the horizontal temperature propagation is quite heterogeneous due to the presence of a network of faults which allows the communication of deep aquifer with shallow aquifer.
At Jebel Aziza, located west of the study area, water flows from the deep aquifer (Continental Intercalary), which has a temperature of 80 degrees, vertically through the F1 fault level to until it reaches the surface reservoir, then mixes with the surface water and continues its flow horizontally and its temperature gradually decreases to 25 degrees.
At the planar sites of the F5 and F7 faults, the same phenomenon occurs, where the warm waters of the deep Continental Intercalary aquifer rise vertically towards the superficial aquifer due to the presence of a thermal gradient, this action is controlled by the hydrodynamic parameters of the deep aquifer.
Groundwater flow is controlled by the tectonic events present in the area (F1, F2, F5 and F7) as well as the hydrodynamic parameters of the CI aquifer. The pressure of the CI aquifer is greater than that of the surface aquifer, allowing groundwater to rise vertically into the surface aquifer.
Underground water flow systems
The geothermal flow pattern in the study area has been summarized by several researchers (Mamou 1990, OSS 2003, Abidi 2004, Agoubi et al. 2015 and Agoubi 2018) based on the hydrodynamic parameters, geochemical compositions, and stable isotopes of the aquifer system as follows, the warm waters of the deep continental aquifer rise rapidly through systems faults and then they later converge in a shallow aquifer; An aquifer whose temperature decreases with flow directions. This pattern is confirmed in this study depending on the water temperature distribution.