# Hydrogeological Parameter Estimation of Confined Aquifer within a Rectangular Shaped Drop Waterproof Curtain

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Drawdown Solution for Flow in a Confined Aquifer of Infinite Extent

#### 2.1.1. Mathematical Model

#### 2.1.2. Solution

_{n}) is defined by

^{2}S/(4Tt), x

_{n}= nπr/M, Ss represents the specific storage of aquifer.

_{n}) can be approximately expressed by

_{0}(·) is the zero-order modified Bessel function of the second kind.

^{2}S/4Tt into Equation (9), one obtains

_{1}= d′ and z

_{2}= d′ + l′ (Figure 1) can be obtained by averaging the drawdown in Equation (7) over this interval and can be written as [2,39,40]).

_{r′}is a constant for a given l′, l, r′, d, d′, and M.

#### 2.2. Drawdown Solution for Flow in a Confined Aquifer within a Fully Penetrated Waterproof Curtain

_{0}is the radial distance from the observation well to the pumping well, r

_{i}(i = 1, 2, …, n) is the distance of an observation well from the image well i.

_{0}. Substitution these values into Equation (18), one can obtain

#### 2.3. Estimation for Hydrogeologic Parameters

_{0}.

## 3. Application for Parameter Estimation Using Field Test Data

#### 3.1. Study Area

#### 3.2. Field Pumping Tests

^{3}/h and 28.0 m

^{3}/h, respectively, and the radial distance r

_{0}from the observation well (H1) and H2 to pumping well (W1) are equal to 42 m and 26 m, respectively. The drawdown records for different single pumping tests are shown in Table 1.

#### 3.3. Parameter Estimation

_{r}can be calculated by Equation (15), and the results are shown in Table 2.

_{0}= 61.24. The values of A and R in Equation (17) can be, respectively, calculated as 0.026 and 5.84 × 10

^{43}. Following the above-mentioned procedure for the straight-line method, one can determine the parameters of the pumping confined aquifer, and the estimated hydraulic conductivity and storage coefficient are K = 25.96 m/d and S = 0.0011, respectively. In addition, in order to verify the correctness of the newly developed solution and the straight-line method, Figure 6 shows the drawdown predicted by the estimated hydraulic parameters and the observed values at relatively long pumping times, and the results are shown the reliability of the methods in this study.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic representation of an infinite confined aquifer partially penetrated by pumping and observation wells.

**Figure 6.**Comparison of the theoretical drawdown obtained by the newly estimated parameter and the measured field data for observation well H2.

Pumping Time (t/min) | Observation Well (H1) | Observation Well (H2) |
---|---|---|

Drawdown (s/m) | Drawdown (s/m) | |

0 | 0 | 0 |

3 | 0.006 | 0.04 |

10 | 0.09 | 0.06 |

15 | 0.122 | 0.07 |

20 | 0.138 | 0.08 |

25 | 0.152 | 0.1 |

30 | 0.173 | 0.11 |

60 | 0.215 | 0.17 |

90 | 0.26 | 0.3 |

120 | 0.42 | 0.5985 |

150 | 0.58 | 0.7801 |

180 | 0.675 | 0.8504 |

210 | 0.84 | 1.0529 |

240 | 0.935 | 1.2037 |

270 | 0.997 | 1.2545 |

300 | 1.044 | 1.2681 |

l/M | r/M | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

2 | 1 | 1/3 | 0.1 | 1/30 | 0.01 | 0.005 | 0.002 | 0.001 | 0.0005 | |

0.1 | 0.00034 | 0.0130 | 0.4390 | 3.3949 | 8.6047 | 15.2123 | 19.1007 | 24.2574 | 28.1615 | 32.0661 |

0.3 | 0.0012 | 0.0383 | 0.5674 | 2.6123 | 5.6922 | 9.5087 | 11.7527 | 14.7297 | 16.9837 | 19.2382 |

0.5 | 0.0020 | 0.0630 | 0.8501 | 2.9352 | 5.3649 | 8.1824 | 9.8214 | 11.9919 | 13.6346 | 15.2775 |

0.7 | 0.0022 | 0.0702 | 0.9672 | 3.3991 | 6.1969 | 9.3944 | 11.2468 | 13.6980 | 15.5527 | 17.4075 |

0.9 | 0.0018 | 0.0570 | 0.7689 | 2.6914 | 4.9703 | 7.6265 | 9.1730 | 11.2214 | 12.7718 | 14.3223 |

Group | r_{1} | r_{2} | r_{3} | r_{4} | r_{5} | r_{6} | r_{7} | r_{8} | r_{9} | r_{10} |

No. 1 | 135.43 | 114.00 | 109.18 | 101.90 | 102.47 | 113.02 | 118.65 | 74.09 | 64.68 | 43.70 |

No. 2 | 148.58 | 134.00 | 131.40 | 130.21 | 132.11 | 144.75 | 150.47 | 79.68 | 68.26 | 34.05 |

r_{11} | r_{12} | r_{13} | r_{14} | r_{15} | r_{16} | r_{17} | r_{18} | r_{19} | r_{20} | |

No. 1 | 57.71 | 66.38 | 98.75 | 267.42 | 257.23 | 255.13 | 252.11 | 252.34 | 256.80 | 259.33 |

No. 2 | 31.16 | 40.78 | 76.04 | 241.96 | 233.30 | 231.81 | 231.14 | 232.22 | 239.63 | 243.13 |

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**MDPI and ACS Style**

Li, Y.; Xie, W.; Wang, H.; Peng, B.; Xiong, F.; Zhu, C. Hydrogeological Parameter Estimation of Confined Aquifer within a Rectangular Shaped Drop Waterproof Curtain. *Water* **2023**, *15*, 356.
https://doi.org/10.3390/w15020356

**AMA Style**

Li Y, Xie W, Wang H, Peng B, Xiong F, Zhu C. Hydrogeological Parameter Estimation of Confined Aquifer within a Rectangular Shaped Drop Waterproof Curtain. *Water*. 2023; 15(2):356.
https://doi.org/10.3390/w15020356

**Chicago/Turabian Style**

Li, Yi, Wentao Xie, Hongwei Wang, Bin Peng, Feng Xiong, and Chun Zhu. 2023. "Hydrogeological Parameter Estimation of Confined Aquifer within a Rectangular Shaped Drop Waterproof Curtain" *Water* 15, no. 2: 356.
https://doi.org/10.3390/w15020356