Numerical solution to the problem of two-phase filtration with heterogeneous coefficients by the finite element method

  • Vasilyeva Maria V., vasilyeva_mv@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42, Kulakovsky St., Yakutsk 677000, Russia
  • Prokopiev Grigorii A., reilroot@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42, Kulakovsky St., Yakutsk 677000, Russia
Keywords: porous medium, two fasefiltration, finite elements method, Galerkin method, numerical simulation

Abstract

We consider the process of filtration of a two-phase fluid in a porous, heterogeneous medium. This process is described by a coupled system of equations for saturation, filtration rate, and pore pressure. We consider mathematical models with and without capillary forces, in the presence of which, for saturation, we have a nonstationary convection-diffusion equation. Since this process is characterized by a significant predominance of the convective term in the equation for saturation, countercurrent approximations are used by adding non-uniform artificial diffusion. Speed and pressure are approximated using a mixed finite element method. The results of numerical calculations for a two-dimensional case with strongly heterogeneous permeability coefficients of a porous medium are presented. Several cases of relative fluid permeability associated with linear and nonlinear coefficients and the presence of capillary forces are
considered.

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How to Cite
Vasilyeva, M. and Prokopiev, G. ( ) “Numerical solution to the problem of two-phase filtration with heterogeneous coefficients by the finite element method”, Mathematical notes of NEFU, 24(2), pp. 46-62. doi: https://doi.org/10.25587/SVFU.2017.2.9245.
Section
Mathematical Modeling