矩形边界越流承压含水层中非完整井稳定流解析解

Analytical Solutions of Steady Flow Toward a Partially Penetrating Well in a Rectangular Leaky-Confined Aquifer

针对矩形边界越流承压含水层中非完整井抽水引起的复杂地下水流动问题,建立了直角坐标系下越流承压含水层非完整井稳定流数学模型.通过对地下水流动计算模型的有限Fourier变换和有限Fourier变换域降深函数的逆变换,提出了不同类型边界条件下越流承压含水层非完整井三维稳定流降深解析解.在验证降深解析解正确性的基础上,通过降深解析解计算精度的分析,并结合非完整井抽水条件下含水层地下水流动特性,给出了降深解析解满足计算精度要求的计算项数取值.探讨了含水层正交各向异性、抽水井完整性、井位布置等因素对含水层降深和地下水流动的影响规律,并利用工程案例阐明了降深解析解的工程适用性.

For the complicated problem of groundwater flow to a partially penetrating well in a rectangular confined aquifer,a mathematical model describing the groundwater flow to a partially penetrating well pumped at a constant rate in a rectangular leaky-confined aquifer,was established.The analytical solutions of the 3D steady flow in the Cartesian coordinate system under different boundary conditions,were derived through the finite Fourier transform and the inverse transform.After the verification of the analytical solution of drawdown,the number of calculation items satisfying the calculation accuracy requirement was given,based on the analysis of the calculation accuracy of the analytical solution and the characteristics of the groundwater flow to a partially penetrating well.Moreover,the effects of orthotropy,well integrity and well location on the drawdown and seepage fields,were discussed.The engineering examples demonstrate the applicability of the proposed analytical method.