A fractional Darcian model‐based analytical solution for non‐Darcian flow toward a fully penetrating well in a confined aquifer

Abstract

AbstractThe Forchheimer and Izbash equations have been long employed to investigate the behavior of non‐Darcian flow toward a well in various aquifer systems, but both two equations inevitably introduce problems such as more or less empirical nature, and dimensional unbalance. Therefore, this work makes the attempt to introduce the fractional Darcian model for characterizing the non‐Darcian behavior flow toward a fully penetrating well in a confined aquifer instead of the Forchheimer and Izbash equations. In this study, a fractional Darcian model‐based analytical solution in the time domain is obtained by means of Laplace transform and linearization approximation. The proposed analytical solution of this study can be readily reduced to the classical Theis solution for Darcian flow. Meanwhile, the late‐times and steady‐state analytical solutions for non‐Darcian flow described using the fractional Darcian model are also developed. Moreover, a comparison with previous analytical solutions shows that the newly derived analytical solution in this study is sufficiently accurate at later times. The influences of different parameters on transient drawdown are investigated. The results indicate that the fractional derivative order and hydraulic conductivity have a large influence on drawdown compared with other parameters. The introduction of fractional Darcian model in this study could also provide potential application for further investigations of non‐Darian flow behavior toward fully or partially penetrating wells in different aquifer systems, which can be very beneficial for hydrology and other related fields.