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

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 Stiffest 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 lzbash 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.

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