Multi-scale flow patterns during immiscible displacement of oil by water in a layer-inhomogeneous porous media

This paper presents the results of numerical study of the relationship between micro-and macroscale flows during immiscible displacement in a two-layer porous medium. A feature of the proposed approach is the allowance for large-scale capillarity induced flow due to curvature of the displacement front in macro-inhomogeneous porous medium. The physical mechanisms determining the development of viscous instability in a layer-inhomogeneous porous medium are considered, the methods for suppressing viscous fingers formation based on the stabilization of the displacement front due the action of capillary forces are proposed.

Analytical Solution of the Cauchy Problem for a Nonstationary Three-dimensional Model of the Filtration Theory

This paper is devoted to the study of the Cauchy problem for a system of differential equations describing the unsteady flow of a compressible fluid in a homogeneous and inhomogeneous porous medium with a general nonlinear filtration law in three-dimensional space. In the work using the methods of four-dimensional mathematics, a special four-dimensional space of space and time coordinates was developed, as well as a functional space of regular functions, and analytical conditions were obtained on the general form of the nonlinear filtration law for which the Cauchy problem has a solution.