Capillary-gravitational separation of immiscible fluids in porous media

The redistribution of liquid phases under the action of capillary and gravitational forces determines the course of several processes in oil and gas extraction technology: the migration of hydrocarbons, and the formation of deposits, subsurface storage of oil and gas in water-saturated structures. The solution of the dynamic problem and comparison of this solution with the asymptotic solution makes it possible to determine, in addition to the detailed phase distribution, the duration of the intense segregation period, i.e., the time during which the segregation is essentially completed.We consider the problem of the dynamics of the one-dimensional segregation of immiscible liquids in a horizontal sheet-like stratum. In this case the process is described by nonlinear differential equations of the parabolic type with discontinuous coefficients and nonlinear boundary conditions. A distinctive feature of this equation is the existence of solution discontinuities at the points of discontinuity of the equation coefficients. A numerical method for solving the problem is proposed in this article and realized on a computer. We also consider dynamic segregation in a uniform stratum. The asymptotic solution for t is indicated for each of the dynamic problems. The criterion is found for the existence of contact between the phases.The authors wish to thank T. V. Startsev and L. Kh. Aminov for assistance in performing the calculations.