The one-dimensional problem of the nonpiston type displacement of a gas by water, taking account of capillary forces

Abstract

The description of the process of the nonpiston type displacement of a gas, taking account of capillary forces, is brought down to the solution of a boundary value problem for a system of nonlinear differential equations in partial derivatives, with certain initial and boundary conditions. Under determined conditions, the problem is found to be self-similar, and comes down to the solution of a system of ordinary differential equations. For this case, calculations are made of the distribution of the pressure and the degree of saturation along the length of a stratum, with different functional dependences of the phase permeabilities for water and gas, as well as of the capillary pressure on the degree of saturation. For purposes of comparison, calculations were also made for variants without taking account of capillary forces and without taking account of compressibliity. The results obtained permit drawing a conclusion with respect to the decisive effect of the above functional dependences considered in combination, on the character of the displacement