Estimating Hydraulic Parameters of Aquifers Using Type Curve Analysis of Pumping Tests with Piecewise-Constant Rates
Abstract
:1. Introduction
2. Methodology
2.1. Analytical Solution
2.2. Type Curve Method
- (1)
- Plot the measured drawdown–time curve in a log–log graph.
- (2)
- Determine φi and βi, and prepare a series of type curves with different t1,D values in a log–log graph of the same scale as the measured curve.
- (3)
- Similar to Theis’s matching technique, match the measured drawdown–time curve with one of the type curves and choose the best matching curve.
- (4)
- Record the corresponding t1,D value, select a match point, and read the corresponding coordinates of s, t, sD, and tD.
3. Field Application
3.1. Background
3.2. Analysis of In Situ Pumping Test
4. Discussion
5. Conclusions
- (1)
- The study introduced a new dimensionless transformation formula to simplify the analytical solution of variable-rate pumping tests, and a piecewise-constant function was further used to approximate the time-varying pumping rate records. Type curve analyses revealed that the time–drawdown curve of the first step was consistent with the Theis curve. However, the type curves of the subsequent steps deviated from the Theis curve and were associated with the first dimensionless inflection time (t1,D), which depended on the K and Ss of the confined aquifers. A large t1,D resulted in a faster time for a sudden turn in the drawdown.
- (2)
- A new type curve method was proposed to handle situations where the real pumping rate varies in a complicated pattern over time. One unique feature of this method is that the type curves depend on the pumping conditions rather than the observation conditions, making it applicable to drawdown data collected from various observation wells during a single pumping test. Furthermore, this new method could also be used to analyze recovery drawdown data by setting a zero pumping rate value for the corresponding shutdown period.
- (3)
- The hydraulic conductivity (K) and specific storage (Ss) of the first and second confined aquifers at the field site were estimated using the pumping rate and drawdown records from four real pumping tests. The estimation results showed that the hydraulic parameters obtained from the newly proposed type curve method were close to the calibrated results reported by PEST, indicating the reliability and robustness of this new method. Moreover, the K estimates were further verified by comparing them with lithology-based results. The geometric means of K and Ss were 6.62 m/d and 3.16 × 10−5 m−1 for the first confined aquifer and 0.92 m/d and 2.34 × 10−4 m−1 for the second confined aquifer.
- (4)
- The field pumping test results showed that the actual pumping rate may have an uncontrollable and short-duration decreasing trend at the early times of each step, resulting in uncertainty in the evaluation of aquifer hydraulic parameters. In addition, the heterogeneity of natural aquifers and the non-uniformity of their thickness also led to differences in the estimated hydraulic parameters of different observation wells in the same pumping test. Future studies will focus on characterizing the heterogeneity of aquifer systems from multiple pumping test data based on more realistic and refined pumping models.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Test No. (Aquifer) | Obs. Well | t1,D | Coordinate Values | K | Ss | |||
---|---|---|---|---|---|---|---|---|
tD | sD | t (d) | s (m) | |||||
1 (2nd CA *) | ow1-1 | 500 | 516.72 | 7.04 | 1.74 | 6.53 | 0.83 | 4.47 |
ow1-2 | 200 | 213.26 | 6.02 | 1.79 | 5.53 | 0.84 | 1.26 | |
2 (2nd CA) | ow2-1 | 1000 | 1020.38 | 8.73 | 2.13 | 3.66 | 1.07 | 3.58 |
ow2-2 | 200 | 217.55 | 7.05 | 2.27 | 3.55 | 0.89 | 1.66 | |
3 (1st CA) | ow3-1 | 20,000 | 481,359.64 | 30.96 | 1.06 | 0.54 | 4.98 | 0.02 |
ow3-2 | 1000 | 24,185.94 | 23.10 | 1.06 | 0.34 | 5.90 | 0.05 | |
4 (1st CA) | ow4-1 | 1000 | 1754.08 | 4.11 | 4.06 | 1.23 | 2.01 | 7.47 |
ow4-2 | 300 | 569.65 | 3.56 | 4.07 | 1.07 | 2.01 | 2.55 |
Test No. (Aquifer) | Observation Well | K (m/d) | Ss (×10−4 m−1) | CE |
---|---|---|---|---|
1 | ow1-1 | 0.84 [0.81,0.87] a | 4.28 [3.67,4.99] | 0.993 |
(2nd CA *) | ow1-2 | 0.87 [0.83,0.91] | 1.22 [1.03,1.44] | 0.988 |
2 | ow2-1 | 1.07 [0.99,1.14] | 3.75 [2.66,5.28] | 0.973 |
(2nd CA) | ow2-2 | 0.92 [0.85,0.98] | 1.53 [1.17,2.01] | 0.972 |
3 | ow3-1 | 4.96 [4.30,5.62] | 0.02 [0.004,0.08] | 0.933 |
(1st CA) | ow3-2 | 6.28 [5.73,6.83] | 0.04 [0.02,0.08] | 0.958 |
4 | ow4-1 | 1.98 [1.85,2.11] | 8.85 [6.63,11.81] | 0.819 |
(1st CA) | ow4-2 | 2.20 [2.03,2.37] | 1.78 [1.30,2.43] | 0.743 |
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Li, Y.; Zhou, Z.; Zhuang, C.; Dou, Z. Estimating Hydraulic Parameters of Aquifers Using Type Curve Analysis of Pumping Tests with Piecewise-Constant Rates. Water 2023, 15, 1661. https://doi.org/10.3390/w15091661
Li Y, Zhou Z, Zhuang C, Dou Z. Estimating Hydraulic Parameters of Aquifers Using Type Curve Analysis of Pumping Tests with Piecewise-Constant Rates. Water. 2023; 15(9):1661. https://doi.org/10.3390/w15091661
Chicago/Turabian StyleLi, Yabing, Zhifang Zhou, Chao Zhuang, and Zhi Dou. 2023. "Estimating Hydraulic Parameters of Aquifers Using Type Curve Analysis of Pumping Tests with Piecewise-Constant Rates" Water 15, no. 9: 1661. https://doi.org/10.3390/w15091661
APA StyleLi, Y., Zhou, Z., Zhuang, C., & Dou, Z. (2023). Estimating Hydraulic Parameters of Aquifers Using Type Curve Analysis of Pumping Tests with Piecewise-Constant Rates. Water, 15(9), 1661. https://doi.org/10.3390/w15091661