Draining of Liquid from a Well into a Porous Medium

Abstract

Capillary suction and gravity force liquid from a well into a surrounding porous medium. The position of the wet/dry boundary is determined, together with the time-dependent level of the liquid in the well. Two models for the structure of the porous medium are employed. In the first, a one-dimensional model, the medium is formed from an assembly of parallel capillary tubes. In the two-dimensional second model, the capillaries form a horizontally stratified network, and Darcy's law holds in each horizontal plane. In both cases, the pressure in the porous medium at any instant depends on both the liquid level in the well and the position of the wet/dry interface, and the problem is essentially nonlinear. Solutions are determined asymptotically and numerically. When the contact angle for the liquid in a capillary is obtuse, gravity and capillary forces are in opposition, and liquid that enters the capillary may later be withdrawn. Some solutions exhibiting this behaviour are presented.