Regional Flow Influenced Recirculation Zones of Pump‒and‒Treat Systems for Groundwater Remediation with One or Two Injection Wells: An Analytical Comparison
Abstract
:1. Introduction
2. Conceptual Model and Complex Potential Functions
2.1. Simplified Conceptual Model
2.2. Complex Potential Function
2.3. Streamline and Branch Cuts
3. Analytical Solutions of 1e1i System
3.1. Dimensionless Functions
3.2. Stagnation Points
3.3. Recirculation Zone
4. Analytical Solutions of 1e2i System
4.1. Dimensionless Functions, Stagnation Points and Divide Lines
4.2. Patterns of Flow Zones
- (1)
- Both RZs of the injection wells I1 and I2 are developed, as shown in zones III1 and III2 in Figure 7a. The extraction well gains water from zones I (regional flow) and RZs. The injection wells I1 and I2 also contribute water to zones II1 and II2, respectively, for the downgradient regional flow. The discharge rates, Q12, Q13, and Q23, satisfy the following relationship:
- (2)
- Only the RZ of injection well I1 exists, as zone III1 in Figure 7b. The flow contributed from the injection well, I2, totally joins the downgradient regional flow behind S3. The discharge rates, Q12, Q13, and Q23, satisfy the following relationship:
- (3)
- Only the RZ of the injection well I2 exists, as zone III2 in Figure 7c. The flow contributed from this injection well totally joins the downgradient regional flow behind S2. The discharge rates, Q12, Q13, and Q23, satisfy the following relationship:
- (4)
- Both RZs of the injection wells I1 and I2 do not exist, as shown in Figure 7d. Water contributed from the injection wells totally joins the downgradient regional flow. The discharge rates, Q12, Q13, and Q23, satisfy the following relationship:
4.3. Dependency of Recirculation Ratios on Parameters
4.4. The Impact of Water Table Limitations
5. Comparison Analyses and Discussions on a Synthetic Example
5.1. Hydrogeological Conditions
5.2. RZs and Recirculation Ratios When α = 0 and α = π
5.3. Sensitivity to the Angle of Regional Groundwater Flow
6. Conclusion Remarks
- (1)
- For the 1e/1i system, the existence of the RZ and the recirculation ratio (η) depend on the angle (α) and relative rate (qD) of the regional flow. When the direction of the regional flow is close to the path from the injection well to the extraction well (α ≈ 0), the RZ exists with a η value that is close to 1. Larger qD and α values generally lead to smaller η value;
- (2)
- For the 1e/2i system, the patterns of RZs and the recirculation ratio depend on α, qD and the relative distance between the two injection wells (B). The 1e/2i system is equal to the 1e/1i system when B = 0. In general, an increase in the B value may reduce the integrity of RZs or take away one or two RZs and lead to a decrease in the recirculation ratio, especially when α is close to 0 or π;
- (3)
- Water table limitations in the extraction and injection wells yield a maximum allowable pumping rate for the PAT system and then lead to an upper bound on the recirculation ratio. The 1e/2i system generally has a higher allowable pumping rate than the 1e/1i system;
- (4)
- A special zone of α may exist for the sake of producing RZs in the 1e/2i system, even leading to a larger recirculation ratio than that of the 1e/1i system.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Theme | Elements and Parameters | Symbol | Value |
---|---|---|---|
Aquifer conditions | Hydraulic conductivity of the aquifer | K | 5 m/d |
Regional groundwater flow rate | q0 | 0.075 m2/d | |
Regional groundwater flow direction | α | 0 ≤ α ≤ π | |
Ground surface elevation | zsurf | 20 m | |
Aquifer bottom elevation | zbot | 0 m | |
Initial water level at (x = 0, y = 0) | href | 15 m | |
Water level limitations | Allowed highest water level | hmax | 18 m |
Maximum discharge potential | Φmax | 810 m3/d | |
Allowed lowest water level | hmin | 10 m | |
Minimum discharge potential | Φmin | 250 m3/d | |
Wells | Location of the extraction well | d | 20 m |
Well radius | re = ri | 0.1 m | |
Half the distance between injection wells | b | ≤20 m | |
Flow rate of the extraction well | Q | <1000 m3/d |
Scenario | PAT System | Cases | b (m) | qmin | Qmax (m3/d) | Q (m3/d) | η |
---|---|---|---|---|---|---|---|
α = 0 | 1e/1i system | C00 | 0 | 0.0365 | 258 | 20 | 0 |
1e/2i system | C01 | 10 | 0.0292 | 323 | 20 | 0 | |
1e/2i system | C02 | 20 | 0.0296 | 319 | 20 | 0.93 | |
α = π | 1e/1i system | C10 | 0 | 0.0285 | 258 | 20 | 0.41 |
1e/2i system | C11 | 10 | 0.0286 | 329 | 20 | 0.40 | |
1e/2i system | C12 | 20 | 0.0290 | 325 | 20 | 0.38 |
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Zhang, S.; Wang, X.-S. Regional Flow Influenced Recirculation Zones of Pump‒and‒Treat Systems for Groundwater Remediation with One or Two Injection Wells: An Analytical Comparison. Water 2023, 15, 2852. https://doi.org/10.3390/w15152852
Zhang S, Wang X-S. Regional Flow Influenced Recirculation Zones of Pump‒and‒Treat Systems for Groundwater Remediation with One or Two Injection Wells: An Analytical Comparison. Water. 2023; 15(15):2852. https://doi.org/10.3390/w15152852
Chicago/Turabian StyleZhang, Shuai, and Xu-Sheng Wang. 2023. "Regional Flow Influenced Recirculation Zones of Pump‒and‒Treat Systems for Groundwater Remediation with One or Two Injection Wells: An Analytical Comparison" Water 15, no. 15: 2852. https://doi.org/10.3390/w15152852