Flow to a partially penetrating well with variable discharge in an anisotropic two-layer aquifer system
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2019 A general analytical model for the problem of variable discharge of groundwater from a well in an anisotropic two-layered aquifer system is developed by taking account of the interface flow between the two layers. The well of infinitesimal radius partially penetrates the lower layer and is pumped at a variable discharge. The horizontal as well as vertical flows in both layers are included, and importantly, the effects of constant-head (Case 1) and no-flux (Case 2) boundaries at the top of the upper layer are considered. Laplace domain solutions for drawdown in dimensionless form are derived with the help of Hankel transform, and are inverted to the time domain numerically. The drawdown characteristics induced by an exponentially decayed rate of pumping are discussed, and sensitivity analysis is also performed to explore the influence of different parameters on drawdown characteristics. The results show that the drawdown around a partially penetrating well in the lower pumped layer induced by an exponential decreasing pumping rate usually contains three stages. The effect of anisotropy and well configuration have great influences on the drawdown distribution near the pumping well, and the horizontal flow and storativity of the upper (unpumped) layer cannot be ignored in determining the upper aquifer drawdown. The sensitivity analysis also illustrates that the dimensionless drawdown in the lower pumped layer is very sensitive to well configuration parameters all the time. It is only sensitive to the hydraulic parameters of the lower aquifer for Case 1 and to the hydraulic parameters of the lower layer and the specific storage of the upper layer at late times. The dimensionless drawdown of the upper layer is not sensitive to the variable well discharge parameters over the whole pumping period, and is not sensitive to the storage parameters of both layers for Case 1. However, the drawdown in the upper layer is sensitive to all the hydraulic parameters and well configuration parameters for Case 2 at late times.
