Numerical research of permeability dependence of porosity in the media formed by regular structure channels

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

Roman S. Saburov, Master’s Degree Student, Institute of Mathematics and Computer Science, Tyumen State University

Abstract:

A porous medium, whose channels have a complex shape and are formed by regular structures, is considered in the article. The authors present a method to determine the permeability of a medium by direct hydrodynamic modeling. The fluid rate is calculated by solving the system of Navier–Stokes equations in the amount of one pore. Then, with the help of Darcy’s law, the permeability of the porous medium is determined. Numerical implementation is carried out in conjunction of open software packages: SALOME–OpenFOAM–Paraview. The geometry of the pore space and the computational mesh are designed with the help of SALOME software package. The calculations are performed with the OpenFOAM package. Visualization of calculations is implemented in the package Paraview. Verification of the solver is carried out on the test case of Poiseuille flow. The article shows that the degree of overlapping spheres permeability decreases rapidly with the reduction of porosity. A close agreement between the results of calculations and analytical lower estimator for the permeability is given in the article by Igoshin D.E., Nikonova O.A., Mostovoy P.Ya. which is the first quoted in the paper.

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