2.3 Permeability Estimation
Regarding the description of Vogt et al. (2014), two types of potential field equations are connected by the Darcy velocity formula:
\(\sigma\nabla^{2}\psi=-\text{ρg}Q_{V}\left(K\right)K\nabla^{2}\text{h\ }\)(2.18)
Among them, the spatial change of the pressure \(p\) (Pa) denotes the change of the hydraulic head \(p=\text{ρg}\nabla h\). When estimating the permeability \(K\), it is set as an ideal pressure distribution in a uniform half-space. Different pressure distributions can also be applied to the terrain surface or the stratum according to the specific conditions.
\(\frac{{\sigma\nabla}^{2}\psi}{\nabla^{2}h}=-\frac{\text{ρg}}{\mu}Q_{V}\left(K\right)K=-\sigma c\left(K\right)\)(2.19)
c( K) denotes the sedimentary coupling coefficient on permeability, which is related to the ratio of potential and pressure and is equal to \(\frac{\psi}{h}\text{.\ }\mu\) is the viscosity of the underground medium. Considering the dependence of\(Q_{V}\left(K\right)\) on permeability, we can know:
\(\log_{10}\sigma c\left(K\right)\mu=-9.2+0.18\log_{10}K\) (2.20)
Combining the above equations, a coupling coefficient value that depends on \(K^{0.18}\) can be obtained. Although the permeability dependencies of the coupling coefficient reported in the literature are not as strong as in \(K\) (Jardani & Revil, 2009), Vogt et al. (2014) applied it for study to see maximal effects resulting from permeability dependent coupling. The main workflow of SP inversion and permeability estimation is shown in Figure.1.
3 Groundwater Flow Monitoring during a Field Pumping Experiment
3.1 Groundwater Table Hydrological Monitoring
The experiment site is in the hydrological observation site of Jilin University (Figure 2). The ERT survey line is 59 m with an electrode space of 1 m. There are four shallow water wells (C6, Ch2, C1, Ch1), and the pumping test is conducted at the well Ch2.
A standard procedure consists of a continuous pumping for 12 hours at well Ch2. After pumping stops, the groundwater level recovers to the normal within the next 12 hours. Figure 3 visualizes the groundwater level depth in the C6, Ch2, C1, and Ch1 wells along the ERT line. The initial groundwater level is about 2.5 m at 3:30 pm. As pumping water, the depth of the groundwater level in Ch2 declines and reaches a trough value of 6.5 m around 4:50 am (10 hours later). After stopping pump water, the groundwater level slowly returns to the initial depth by groundwater recharge. The water level of wells C6 and Ch1 is slightly changed. The water level in C1 well shows a significant variation after pumping is stopped. It indicates that the recharging process affects the groundwater level around the well C1.
3.2 ERT Monitoring Test
The 2D ERT time-lapse survey uses the Wenner-Schlumberger array. There are 60 electrodes with an electrode space of 1 m. The recorded apparent resistivity data are inverted using RES2DINV software (Loke, 2006). Figure 4 shows the background ERT result and source current density inverted by SP data before the pumping test. The first low-resistivity layer is about 0~2.5 m, which corresponds to a high-permeability topsoil layer. The current source density at the same depth also shows high values, which reflects the high flow value in the shallow low-resistance area. It is the natural characteristic of low-resistivity soil. Below 2.5m, it is an unsaturated clay layer. The low resistivity zone in the middle part indicates the groundwater distribution in the shallow well.
The time-lapse ERT surveys last more than 20 hours, and the time interval between subsequent surveys is 1 hour. The recorded data are pre-processed and inverted by the RES2DINV software to obtain the resistivity tomography profile in Figure 5 (left). The time-lapse resistivity tomograms have good consistency, which indicates the reliability of the raw data. Figure 5 (right) is the time-lapse resistivity variation, which is obtained by subtracting ERT results from the background ERT shown in Figure (4). It shows significant spatial and temporal resistivity changes in the pumping area. With the pumping process, the low-resistivity zone gradually becomes deeper. It indicates that the groundwater level declines. Similarly, after pumping water is stopped, the groundwater level steadily recovered, and the low-resistivity at the bottom of the formation increased.
Figure 6 shows the results of resistivity changes over time for wells Ch2 and C1 at different depths. The resistivity changes around the two wells are similar to the hypothetical formation structure. We believe that there are two types of groundwater recharge zones, which have played a key role in different models. In the pumping process, the water level in well Ch2 dominates, and the recharge zone is about 3 m to 6 m. However, the recharge range of well C1 is only 3 m to 4 m, and the resistivity change is consistent with the groundwater level record. In the recovery process, the supply area of well Ch2 is below 6 m, showing a trend from low to high, while the supply range of well C1 is below 4 m, showing a continuous increase in resistivity changes.
3.3 SP Signal Monitoring
The self-potential signal in the pumping test depends on the movement of the groundwater flow. The SP signals are naturally occurring electric field measured at the ground surface with non-polarisable electrodes in the ERT survey line, and the time-lapse interval is 1 hour.
3.3.1 Synthetic Model SP Test
In order to test the SP signal in the pumping process, we first build a synthetic model according to the pumping experiment (Figure 7). The model (50m × 15m) has three layers. Two drill pipes are set up to simulate the pumping and recovery process. The permeability and conductivity parameters of the model are in Table 1.
A fluid pressure of 1,000 KPa is applied on the surface. Regarding the electrical boundary conditions, Neumann conditions at the surface ensure that potential anomalies can be responded to at the surface. Considering that the bottom permeability of the model is extremely low, and the left and right boundaries are far from the channel, the Dirichlet conditions are given to simulate zero at infinity. The potential underground anomaly obtained through the forward modeling problem is shown in figure 8 (up) and figure 9a. The SP amplitude response has significant changes at different times. It demonstrates that the rise of groundwater has positive self-potential anomalies, while the abnormal negative signals are caused by drawdown. The amplitude of the SP signal decreases with growing distance from the injection well, which roughly matches the prediction of radial flow in a homogeneous medium around an infinite source.
Regarding the inversion problem, the SP signal is used to retrieve the current source density js . A regularization smoothing term is added to the calculation process to solve the ill-posedness of the potential problem. Where calculate the potential field of the jsterm (Cardarelli, 2019), we added the conductivity model used in the forward modeling as a constraint term to invert the potential underground distribution (Figure 9b) and the surface SP signal (Figure 8(bottom)). Comparing the anomalous distributions obtained from the two sets of problems, both can adequately characterize the potential response during the decline and rise of the water level, and the results obtained by the inversion of the water level in the bottom part show instability.
3.3 Time-lapse SP Signal in the Pumping Experiment
The surface SP time-lapse measurements during the pumping test with 1 hour time interval are shown in the left column of Figure 10. It shows a significant SP signal variation during the groundwater flow. The change of the real SP data agrees with the conclusion of the above SP synthetic model test. The SP field shows local negative anomalies during pumping, which is the result of groundwater level decline in the well. When pumping is stopped, the potential anomaly drops significantly and shows multiple positive anomalies, indicating that the water flow in the bottom recharge zone penetrates upwards until the pumping equilibrium.
Using the ERT resistivity as a constraint, we estimate the permeability distribution in the test area according to the SP data (right column of Figure 10). Similarly, the electrical boundary conditions are consistent with those of the forward simulation, and the ground surface uses the Neumann boundary condition. The estimated value of permeability information is a scalar quantity, which represents the information state of groundwater flow sensitivity and distribution in the formation. It can be observed that the characteristics of groundwater flow are evident in the two model phases (pumping and recovery), and they are mainly distributed in the shallow formations around well Ch2.
4 Discussion
The ERT and SP results show reliable evidence to describe the groundwater pumping and recharge experiments. In Figure11a, we compare the time-lapse hydrological groundwater level monitoring at well Ch2 to the ERT and SP results. The groundwater level increases from the initial depth (2.5m) to 6.5 m at the pumping water stage (from 3:30 pm to 6:50 am). Then, the groundwater level returns to the initial depth by the groundwater recharge. Since the soil moisture content reduces in the pumping stage, the resistivity increases to the maximum value of 8.4 Ohm.m (Figure 11b). Then, the resistivity decreases to initial value after the groundwater recharge. It is consistent with the groundwater level change in Figure 11a. There is a positive correlation between the groundwater level and the soil resistivity.
The SP field at the same depth near the wellhead (Figure 11c) has a negative correlation with the groundwater level change. The estimated permeability by SP and ERT coupling coefficient is in Figure 11d. The primary relationship between the permeability and moisture content in unsaturated soil is that the high moisture content corresponds to low permeability (Gómez et al., 2019; Miao et al., 2018). The reason is that increase in water level depth means that the moisture content reduces. Then, the soil porosity will increase with permeability.
The permeability response is not directional, but it shows a derivative change in the water level detection results. The peak value of the pumping period is at 7 pm. The permeability value shows a significant increase with the rapid decline of the water level, and the permeability gradually decreases in the saturated state in the late pumping period. In the same way, within the pumping stops, the rise of the groundwater level causes the permeability to increase. When the water level returns to its original state, the permeability is flat with the background value.
Based on the following discussion, we build the conceptual model to display the groundwater flow characteristics around well Ch2 and well C1 (Figure 12). The process of groundwater flow can be divided into two stages (Figure 12a: pumping and Figure 12b: recovery), and the main layered recharge is concentrated in the changing area of water level. It is clear to see that in the pumping model, the central formation becomes the main recharge area in the well, and in the recovery stage, the deep structure recharges the water to the well. The continuous recharge zone around well C1 corresponds to the low resistivity zone. It can be interpreted as an area of high permeability and high moisture content, both of which provide groundwater recharge.
5 Conclusion
We combined the time-lapse ERT and SP methods to monitor the dynamics in groundwater flow. Groundwater flow infiltrates and transfers between soil particles and pores, and the moisture content affects the formation and other parameters to some extent. The ERT result establishes linkages between the resistivity and moisture content to reveal the change of groundwater flow. Besides, the SP field is sensitive to the groundwater flow by groundwater dynamics. The rise and drawdown of groundwater will produce positive and negative SP field, respectively. The pumping water experiment results demonstrate that the ERT and SP method combined can provide a reliable way to describe the variation of groundwater flow and understand the qualitative relationship between groundwater flow and its geophysical response.
Data Availability Statement
Data associated with this research are available and can be obtained by contacting the corresponding author.
Acknowledgments
This work are supported by the Natural Science Foundation of China (41874134), the Jilin Excellent Youth Fund (20190103142JH) and the China Postdoctoral Science Foundation 2015M571366
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