Two-Phase Fluid Flow in a Model Porous Medium Formed by Axisymmetric Channels of Variable Cross Section

About the author:

Dmitry E. Igoshin, Cand. Sci. (Phys.-Math.), Head of the Reservoir Physics Laboratory, Corporate Center for the Study of Reservoir Systems (Core and Fluids), Gazprom VNIIGAZ (Moscow); Associate Professor, Department of Fundamental Mathematics, Institute of Physics and Technology, University of Tyumen; d.e.igoshin@utmn.ru

Abstract:

The micro-inhomogeneities of the porous medium have a decisive influence on its filtration-capacitive properties, such as porosity, absolute permeability, and relative phase permeability. This fact explains the relevance of a study of multiphase flows in the channels that constitute the porous media. There are several approaches to modeling porous media: periodic structures, filtration theory, percolation theory, and statistical hydrodynamics. The approach based on periodic structures, has several advantages: to determine the reservoir properties of the simulated medium (knowing the geometry of one characteristic pore), it is enough to describe the fluid flow inside, based on analytical estimates or from the results of numerical solution of the system of hydrodynamic equations.

This article considers the features of the flow of a two-phase fluid in axisymmetric channels of variable cross section with periodic boundary conditions. The saturation of each phase depends on the initial distribution of these phases in the channel and does not depend on time. Furthermore, the flow of a two-phase incompressible linearly viscous fluid is calculated numerically based on the Navier-Stokes system of equations. At each time point, the reduced pulse of both phases was determined. The time-averaged value of the reduced pulse in the quasi-periodic flow regime is used to calculate the relative phase permeabilities in the dependence of the initial ratio of the phase saturations.

All calculations are done in open packages. The channel geometry and computational grid are built in the Salome package, the flow is calculated in the OpenFOAM computation package, the visualization of the calculation results is performed in the paraView application.

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