Numerical and analytical estimates of permeability of porous medium formed by channels having rotational symmetry

About the authors:

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

Aleksei Yu. Maksimov, Lead Engineer, CompMechLab® LLC, Peter the Great St. Petersburg Polytechnic University; eLibrary AuthorID, ORCID, maksimov@compmechlab.ru

Abstract:

We examine the porous medium of periodic structure formed by varying-area channels having rotational symmetry. The porosity of the modeling medium is defined. An analytical method for determining the permeability of such medium taking into account variable clearance of the channels is introduced. Using computer modeling, the system of hydrodynamic equations is solved in the volume of a single pore. The permeability of the porous medium is determined using Darcy’s equation at the calculated volume flow of fluid through the pore channel. Computer modeling is carried out by using opensource packages SALOME–OpenFOAM–Paraview. The SALOME package is used to build parametric geometry and computational grid for the channels of the porous medium. The calculations are performed in the OpenFOAM package. Visual representation of the calculation results are presented in the Paraview package. A good quantitative agreement is achieved between the calculation results in the OpenFOAM package and the analytical estimation introduced in the paper. It is shown that with the decrease in porosity and its approaching to the limiting value, the permeability sharply decreases.

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