承压含水层中抽水井附近非达西流的近似解析解

Approximate analytical solution of non-Darcian flow towards the well in confined aquifer

本文将线性化方法和Laplace变换相结合研究承压含水层中单一抽水井附近的非达西流问题,得到了水位降深在抽水后期和抽水稳定阶段的近似解析解,并对抽水后期近似解析解的适用性进行了讨论。通过Stehfest数值Laplace逆变换得到了任意时刻任意位置水位降深的半解析解,并采用数值解对线性化方法所得到的近似解进行了验证。研究结果表明:在抽水后期,水位降深随着Izbash定律中的两个常数的增大而减小;在抽水后期,水位降深近似为时间的幂函数,在抽水稳定阶段,水位降深可以近似为距离的幂函数;在抽水后期,线性化方法所得到近似解与数值解吻合很好,而在抽水初期线性化方法则存在一定误差,会低估水位降深。

By combining the linearization approximation of the non-Darcian flow equation with Laplace transformation a new method for analyzing the non-Darcian flow towards the well in confined aquifer is developed. The analytical solutions of the drawdown at steady state and late times are obtained. The applicability of the solution for late times is discussed. The drawdown at arbitrary moment and distance is obtained by numerical Laplace inversion method named Stehfest method. A finite difference solution for verifying the approximate analytical solution is derived from linearization procedure. The results indicate that the drawdown decreases at late times as the two constants in lzbsh equation increase and is approximately a power function of time. At steady state, the drawdown is the power function of radial distance. The approximate solution obtained from linearization approach is in good agreement with the numerical solution at late times, but error may occur for early times of pumping.