The method of local linearization for the calculation of one-dimensional processes of two-phase flow in porous media

Abstract

The authors consider processes of displacement of one fluid by another in a porous medium for which the corresponding solutions of the Buckley-Leverett problem [1] are nonself-similar because of the inhomogeneity of the initial and/or boundary conditions [2]. The traditional approach to the solution of these problems consists in the use of finite-difference methods or the method of characteristics in various modifications. However, finite-difference methods distort the solutions because of “smearing” of the discontinuities, and the method of characteristics (in the analytical variant for problems with step initial and boundary conditions or in the numerical variant for problems with conditions of the general type) becomes difficult to put into practice if the number of separated fronts (waves)is large.