The Numerical Calculation of Permeability in Two-Dimensional Porous Media with Skeleton of Randomly Arranged Overlapping Disks

About the authors:

Aleksey S. Gubkin, Junior Researcher, Tyumen Branch of Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the RAS; Senior Lecturer, Department of Mechanics of Multiphase Systems, Tyumen State University; alexshtil@gmail.com

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

Dmitry V. Trapeznikov, Mathematical Modeling Engineer, Automation and Digital Modeling Department, University of Tyumen; d.v.trapeznikov@utmn.ru

Abstract:

The article presents the two-dimensional model of a porous medium with random micro-inhomogeneities and the results of numerical calculation of single-phase flow of a Newtonian fluid through a model porous medium. The results of calculations based on Darcy’s equation allowed to find the absolute permeability coefficients in the longitudinal and transverse directions. The principle of the skeleton constructing the medium is that the region in the form of a rectangle with sides L_x and L_y is randomly cast with disks of random radius in the range from R_min to R_max. The algorithm includes two model parameters: δ_in and δ_out, giving the minimum imposition of overlapping disks and the minimum distance between the non-overlapping discs. Thus, the skeleton of the porous medium was formed until achieving the preassigned value of porosity. Then the pore space is obtained by subtracting the skeleton from the treated area. The geometry of the problem and the computational grid were built in open package Salome, the numerical solution of the Navier-Stokes equations for a given pressure drop at the boundaries of the area was considered in the open package OpenFOAM. The difference founded values of the absolute permeability in the longitudinal and transverse directions is no more than half which speaks of the volume of the calculated area being close to the representative.

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