Some Invariant Solutions to Two-Phase Fluid Displacement Problems Including Capillary Effect

Summary Analytical investigation of the two-phase displacement problem that considers capillary force is one of the most important and difficult problems in the theory of fluid flow through porous media. This paper presents some invariant solutions on the subject, including a self-similar solution for the axisymmetric case, a self-similar solution in a linear, isoclinal reservoir that considers the effects of gravity and capillary forces simultaneously, and a progressive wave solution corresponding to a stabilized zone of saturation distribution. The relations and differences among (1) a model that completely includes capillary effect, (2) a model that considers capillary action partially and implicitly (the Buckley-Leverett model), and (3) a model that completely ignores capillary effect are indicated and discussed.