On Coupled Unsaturated-Saturated Flow Process Induced by Vertical, Horizontal and Slant Wells in Unconfined Aquifers
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Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns coupled unsaturated-saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated-saturated flow process and well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation, and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in Laplace domain is derived by the Laplace-finite Fourier transform and the method of separation of variables. It is found that the unsaturated zone has significant effects on the drawdown of pumping test with any angle of inclination of the pumping well, and this impact is more significant for the case of a horizontal well. The effects of unsaturated zone on the drawdown are independent of the length of the horizontal well screen. For the early time of pumping, the water volume drained from the unsaturated zone (W) increases with time, and gradually approaches an asymptotic value with time progress. The vertical well leads to the largest W value during the early time, and the effects of the well orientation become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.
