Gravitational separation of oil and water in beds of limited thickness

Abstract

The problem of the separation of phases of different density in a porous medium in a gravitational field is considered. In describing the segregation process in a very thick bed the capillary pressure may be neglected as compared with the gravitational pressure drop due to the difference in phase densities. In this formulation the problem is a similarity one, but permits a complete analytic investigation with a qualitative analysis of the process on the basis of the exact solutions. The exact solutions of problems of gravitational segregation in beds of limited thickness derived in this study are nonself-similar in character, which distinguishes them from the results for an unbounded bed previously obtained [1]. Taking capillarity into account gives a fuller picture of the phenomenon. A corresponding description and analysis based on numerical solutions are given in [2, 5]. It is characteristic of the problems examined here that for the first-order quasilinear hyperbolic equation describing the segregation process two boundary conditions are formulated. These conditions correspond to the impermeability of the roof and floor of the bed.