| Abstract: | The article describes a method for the solution of the one-dimensional problem of the displacement of petroleum by water taking account of capillary forces; on the basis of the method, in the equations of two-phase filtration it is proposed to use a new, soughtfor function, i.e., the fraction of water in the total flow of liquid. As a result, the problem is simplified, the labor consumption of the calculations is reduced, and it becomes possible to make a qualitative evaluation of the behavior of the solutions, including the analytical justification of a solution with a  stabilized zone. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 83–91, May–June, 1975. |
