Abstract: This paper presents a new kind of method for solving the plane problems of two-phase flow in porous media. The elliptical partial differential equation for pressure distribution is solved by the finite element method, and then the semi-analytical solution for pressure gradient is used to determine the new saturation field according to the existing exact formula describing the saturation propagation along the streamlines. The main distinguishing feature and advantage of this kind of method are the ability to overcome the numerical dispersion which is inherent in the ordinary numerical simulation methods, and thereby, to give a precise and clear-cut position of the saturation discontinuity in the water-oil displacement front. Moreover, the saturation equation, which should commonly be solved simultaneously or alternatively with the pressure equation, is completely avoided, so that the computing time is greatly reduced.

Key words: bifurcation, constraint, singularity theory, nonlinear dynamics, two state variables