Permeability anisotropy in model porous media formed by periodic cubic structures

About the authors:

Kusayko George N., Postgraduate Student, Department of Fundamental Mathematics and Mechanics, Institute of Mathematics and Computer Science, University of Tyumen; Research Engineer, Tyumen Branch Institute of Theoretical and Applied Mechanics named after S. A. Khristianovich, Siberian Branch of the Russian Academy of Sciences; gkusayko@gmail.com; ORCID: 0000-0002-0543-0814
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

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

Abstract:

One way to model porous media is to use periodic structures. The advantage of this approach is the need to describe the fluid flow in the volume of one pore (cell). The flows of a viscous fluid in periodic channel models of porous media formed by structures of three types — cubic simple (CS), cubic body-centered (BCC), and cubic face-centered (FCC) are considered. These structures make it possible to simulate porous media in a wide range of porosity values (1 ÷ 48%).

In the selected structures, three special flow directions are distinguished — along the edge of the cube, along the diagonal of the square (the base of the cube), along the diagonal of the cube. For the chosen directions, the fluid flow was calculated over the entire range of the dimensionless parameter α — the degree of intersection of the spheres, which is a model parameter that characterizes the microheterogeneities of the porous medium and makes it easy to reproduce the geometry of the pore space in the numerical solution of the Navier-Stokes equations in direct hydrodynamic modeling.

Based on the results of calculations based on the Darcy equation, the permeability coefficients for the three main flow directions were determined and an analysis was carried out on the permeability anisotropy in the selected structures. In a simple cubic structure, the greatest permeability is achieved in the 2nd direction (along the diagonal of the base of the cube), the smallest — along the main direction (along the edge of the cube). In a cubic body-centered structure, the highest permeability is achieved in the 3rd direction (along the diagonal of the cube), the lowest — along the 2nd direction (along the diagonal of the base of the cube). In a cubic face-centered structure, the highest permeability is achieved in the 2nd direction (along the diagonal of the base of the cube), the smallest — along the 3rd direction (along the diagonal of the cube).

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