2.3 Permeability Estimation
Regarding the description of Vogt et al. (2014) in the article, two types of potential field equations are connected by Darcy’s 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\(\frac{\psi}{h}\), \(\mu\) 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 K1 (Jardani & Revil,2009), Vogt et al. (2014) apply it for study to see maximal effects resulting from permeability dependent coupling. The main workflow of SP inversion is in Figure.1.
Figure 1: Flowchart of the SP inversion and permeability estimation.
3 Groundwater Flow Monitoring Experiment
We select the appropriate experimental measurement area for artificial pumping to achieve the dynamic change of groundwater flow for a long time. The experiment site is in the hydrological observation site of Jilin University (Figure 2). The ERT survey line is 59 m with electrode space is 1m. There are four shallow wells (C6, Ch2, C1, Ch1), and the pumping test is conducted at the well Ch2.
Figure 2. Photos of the survey area, showing the distribution of the ERT survey lines and the water well locations.
3.1 Groundwater Table Hydrological Monitoring
A continuous pumping process is about 12 hours at Well Ch2. After stopping pumping, 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 around the line. The initial groundwater level is about 2.5m at 3:30 pm. As pumping water, the depth of the groundwater level in Ch2 continuous declines and reaches a peak value (6.5m) around 4:50 am (10 hours later). Then, we stop pump water, and the groundwater level slowly returns to initial depth by groundwater recharge. Both the water level of C6 and Ch1 is little change. The water level in the C1 well has a significant difference after stopping pump water. It indicates that the pumping process only affects the local region around Ch2 and recharges groundwater main from the C1.
Figure 3. Groundwater level monitoring results in the well.
3.2 ERT Monitoring Test
Resistivity tomography is with the Swedish RES2DINV software (Loke, 2006). Figure 4 shows the background resistivity result and source current density inverted by SP data before the pumping test. The first low-resistivity layer is about 0~2.5m, which is surface permeability clay. The current source density at the same depth also shows high values. The current source density, to some extent, 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 sand layer. The low resistivity zone in the middle part indicates that the groundwater distribution in the shallow well.
Figure 4. a) Background ERT results in the experimental area; b) distribution of underground source current density obtained by SP data inversion.
The time-lapse ERT surveys are more than 20 hours, and delayed resistivity data were collected every 1 hour. The collected data is pre-processed and inverted by RES2DINV software to obtain the resistivity tomography profile in Figure 5 (left). The time-lapse resistivity results have good consistency, which indicates that the raw data has stable quality. Figure 5 (right) is the time-lapse resistivity variation, which is obtained by calculating the difference of time-lapse ERT result. 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 is stopped, the water 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 well 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 underground, which have played a key role in different models. In the pumping process, the water level in the CH2 well dominates, and the recharge zone is about 3m 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 water level record. In the recovery process, the supply area of well Ch2 is below 6 m, showing a trend of low to high, while the supply range of well C1 is below 4 m, showing a continuous increase in resistivity changes.
Figure 5. 2D time-lapse ERT tomography results (left) and resistivity variation in a different time (right).
Figure 6.The resistivity curves around Ch2 and C1
3.3 SP Signal Monitoring
The self-potential signal in the pumping test depends on the movement of the groundwater flow. We also collected the time-lapse SP data in the ERT survey line, and the time interval is 1 hour.
3.3.1 Synthetic Model SP Test
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 of soil structure, and 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.
Table 1. Distribution of material parameters for numerical simulation
A fluid pressure of 1,000 KPa is applied on the surface. Regarding the electrical boundary conditions, given Neumann conditions at the surface ensures 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 change at different times. It demonstrates that the rise of groundwater has positive self-potential anomalies, while the abnormal negative signals caused by drawdown. The amplitude of the SP signal decreases with 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 js term (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.
Figure 7. Numerical pumping test with a three-layer soil model
Figure 8. The forward SP data (up) and the inverted SP data (bottom)
Figure 9. (a) The forward potential field of groundwater level changes and (b) the inverted potential field
3.3 Time-lapse SP Signal in the Pumping Experiment
Surface time-lapse SP measurements during a pumping test in the ERT survey line and the time interval is 1 hour (Figure 10a), which shows significant SP signal variation during the groundwater flow. The change of real SP data is in agreement 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 stopping pumping, the potential anomaly dropped significantly, showing multiple positive anomalies, indicating that the water flow in the bottom replenishment zone penetrated upwards until the pumping equilibrium.
Used the resistivity as a constraint, we estimate the permeability distribution in the test area according to the SP data (Figure 10b, Ikardet al., 2018). Similarly, the electrical boundary conditions we choose are consistent with those of the forward simulation, and the ground boundary is 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 Ch2.
Figure 10. (a) Time-lapse SP field in the pumping water experiment,(b) estimated permeability distribution result by SP and ERT coupling coefficient.
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 geophysics result. In Figure 11a, the groundwater level increases from the initial depth (2.6m) to 6 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. In the time-lapse ERT results (Figure 11b), because the soil moisture content reduces in the pumping stage, the resistivity increase to the maximum value. Then, it decreases to normal 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 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 the growth of permeability.
The permeability response is not directional, but it shows a derivative change in the water level detection results. The peak point of the two states during the pumping period is about 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 formation of permeability to increase. When the water level returns to its original state, the permeability is flat with the background value.
Figure 11: a) Time-lapse groundwater level at Well Ch2, b) the resistivity variation around Well Ch2, c) the measured SP signal around Well Ch2, and d) is the estimated permeability by SP and ERT coupling coefficient.
Figure 12: Interpretative scheme of mutual recharge of groundwater flow at pumping and recharge processes.
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. Obviously, in the pumping model, the central formation becomes the main recharge area in the well, and in the recovery stage, the deep formation supplies to the well. The continuous recharge zone around well C1, which 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 Conclusions
In this paper, we combine the time-lapse ERT and SP data to monitor the groundwater flow variation. Groundwater flow infiltrates and transfers between soil particles and pores, and the moisture content affects the formation to some extent and other parameters. 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 change of 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 joint ERT and SP method can provide a reliable result 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.
Acknowledgements
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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