The permeability of the porous medium with a periodic structure branching 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

Olga A. Nikonova, Student, Institute of Mathematics and Computer Sciences, Tyumen State University

Abstract:

The mathematical model of the porous medium with branching channels formed by regular structures is presented. Two types of the structures are considered: body-centered cubic (BC) and face-centered cubic (FC). The skeleton of such medium is formed by spherical segments. These segments adjoin to each other and each segment contains a sphere center. The extent of the spheres intersection is a model parameter that determines the porosity and clearance of the medium. Permeability is defi ned by two parameters: the extent of the spheres intersection and the side of the cube. The pore space is obtained by subtracting the skeleton volume from the total volume. Analytical porosity and clearance dependences of the extent of the spheres intersection were obtained. It is shown, that using considered porous structures, porous medium can be modeled in a wide range of the porosity: (0,6÷32,0)% for the BC structure and (3,6÷26,0)% for the FC structure. The minimum value corresponds to the closed pores. It has been revealed that at fi xed extent of the spheres intersection in the BC structure there are three types of sections and in the FC — four. The section with minimum clearance is the set of channels with the shape close to triangular; four sections for the BC structure and eight sections for the FC structure. On this basis, the lowest analytical estimation for the permeability of considered mediums has been obtained.

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