Transient behavior of the interface of two inmiscible liquids constrained to the porous space between two concentric spheres.

Abstract

The solution for the motion of the interface between two immiscible liquids constrained to a porous space between o concentric spherical surfaces is derived. The fluid motion is produced by the action of gravity and is governed by Darcy's Law. In order to obtain the solution, the problem is simplified in two respects, on the one hand the limiting case of a shell of zero thickness is considered, and on the other one the boundary conditions are linearized. However, a solution is obtained which satisfies the full nonlinear boundary conditions when the interface is plane initially. The time required for the maximum deviation of the interface from the equilibrium position to decrease by the factor 1/ e is determined. The results are compared with those presented previously by Kidder (1956) for a related problem. The origin of tilted oil-water contacts in oil fields is discussed in relation to the results of this study.