A study on Wellbore Flow-rate Solution and Drawdown Solution for a Finite Confined Aquifer with Considering the Effect of Skin Zone
|關鍵字:||地下水;半解析解;定流量試驗;定水頭試驗;拉普拉斯轉換;有限邊界;Groundwater;constant-flux test;constant-head test;Laplace transform;finite confined aquifer|
The constant-head test and constant-flux test are commonly employed for estimating the aquifer parameters in engineering practice. The constant-head test injects or pumps water with a variable flow rate for maintaining a constant hydraulic head in a low-permeability aquifer while the constant-flux test keeps a constant flow rate to record the drawdown distribution from the observation well of a high-permeability aquifer. The solutions for the wellbore flow rate and drawdown at a well with a finite radius in an infinite confined aquifer with or without a skin zone have been reported in the groundwater literature. The effects of well radius and skin zone are negligible if the test period is very long and/or the distance between the observation well and test well is large. However, little attention has been paid to the effect of a finite boundary on the flow-rate and drawdown solutions in the groundwater community. The main objectives of this thesis are first to develop new semi-analytical solutions for exploring the effect of finite boundary on the wellbore flow-rate and drawdown solutions in a confined aquifer where a finite skin zone is present. These solutions are then calculated by the modified Crump algorithm. The Laplace-domain solution can reduce to the existing infinite-domain solution in some special cases. In addition, an approximate solution for small- or large-time condition is useful if the analytical solution is very complicated and not easy to evaluate accurately. The second objective of this thesis is to derive approximate solutions with considering the effect of skin zone in a finite or infinite confined aquifer based on the relationship between the Laplace variable and time. An approximate solution for an infinite confined aquifer with a skin zone can reduce to the solution without a skin zone if the skin is absent. The large-time solution is equal to the steady-state solution for a finite confined aquifer with a skin zone. In addition, this solution can reduce to Thiem’s equation if the skin zone is absent.
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