# Simulation of porous medium in the form of systematically packed intersecting spheres

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy

Release:

Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2014)

Title:
Simulation of porous medium in the form of systematically packed intersecting spheres

Dmitry E. Igoshin, Cand. Sci. (Phys-Math.), Senior Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; Associate Professor, Department of Fundamental Mathematics and Mechanics, Department of Applied and Technical Physics, University of Tyumen; igoshinde@gmail.com

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

Abstract:

A model of a porous medium in the form of systematic packing of intersecting spheres is introduced. Two types of packaging — a primitive cubic and hexagonal primitive one — are considered. The intersection degree of the spheres is a model parametric variable characterizing microinhomogeneity of porous medium. The parameter makes it easy to construct geometry of the pore space in the numerical solution of e Navier-Stokes equations in the direct hydrodynamic simulation. The analytical dependences of porosity and luminal on the degree of intersecting spheres in each package were obtained. Parametric analysis of the mathematical model is done. It has been shown that the packing makes it possible to simulate porous medium in a wide range of porosities: (3,5÷47,6)%, for cubic packing and (16,5÷39)%, for hexagonal one. The minimum value of porosity conforms to the closed pores. There are two types of sections determining permeability and porosity of the porous medium. An analytical lower bound for the permeability of the porous medium is done with the method of equivalent capillary; it allows to find the match between the perfect soil and fictitious soil.

Keywords:

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