Critical Surface Coning Due to a Line Sink in A vertical Drain Containing a Porous Medium

Abstract

The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history.

A spectral modelling approach for fluid flow into a line sink in a confined aquifer

“…Here we extend the previous work of Al-Ali et al [1], who considered the flow into a horizontally confined region that was unbounded below to consider the flow in a finite domain that is bounded both horizontally and below. In this case, if there is no recharge, the flow is necessarily unsteady, and an unsteady spectral method is used to compute the flow.…”

“…Similar studies were undertaken by Lukas et al [11], Muskat and Wychoff [15], McCarthy [12] and Zhang et al [20] with qualitatively similar results in all steady cases. More recently, Al-Ali et al [1] considered the flow into a line sink in a horizontally confined duct that was unbounded below and found both steady and unsteady solutions. Axisymmetric withdrawal solutions for the water coning problem with withdrawal from the upper layer of a stably stratified, two-layer fluid were computed by Lukas et al [11], using an integral equation approach.…”

Simulation of the Movement of Groundwater in an Aquifer

“…Section 3 of the study employs an analytical technique [14] to address the issue raised in Section 2. The Fourier series and its properties are used as the principal tool for problem analysis [15,16]. It was explained in detail how the series' resulting factors are implemented in MATLAB to generate a solution.…”