| Summary: | 博士 === 國立交通大學 === 環境工程系所 === 101 === This thesis develops a mathematical model for describing three-dimensional groundwater flow induced from a vertical well, horizontal well or radial collector well (RC well) in an unconfined aquifer bounded by two parallel streams. A new governing equation with a sink term standing for the well is presented. A simplified free surface equation is used to describe the depletion of water table in the aquifer. The third-type boundary condition is employed for the boundary condition at the interface where a low-permeability streambed is connected to the aquifer. The aquifer we concern is of finite extent; therefore, the head solution of the model, derived by integral transforms, can be expressed in terms of an infinite series with eigenvalues requiring a root-finding scheme such as Newton method. An analytical expression is developed to give initial guesses for the eigenvalues. The solution for stream depletion rate (SDR) describing filtration rate from the streams is acquired based on Darcy’s law and the head solution. The present solution is applied to predict the hydraulic head near a horizontal well or a RC well for the real-world cases. The predicted results are reasonable when compared with the field observed data. With the aid of the present solution, we have found that the gravity drainage of an unconfined aquifer has significant effects on temporal SDR. The curve of temporal SDR tends to be flat due to the gravity drainage during the middle period of pumping time. The vertical groundwater flow described by the free surface equation should be used even for the case of a fully-penetrating well. The SDR will be overestimated if neglecting the vertical flow in the model. Such a result is confirmed by the comparison of SDR predicted from the present solution with that taken from a field SDR experiment executed near Doyleston in New Zealand. Additionally, lateral configurations of a RC well have significant effects on spatial drawdown distributions. The largest drawdown occurs right at the center of a RC well before the filtration and moves landward once the filtration starts to recharge the aquifer.
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