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

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
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.

References:

1. Entov, V.M. Filtration theory. Sorosovskii obrazovatel'nyi zhurnal — Soros Education Journal. 1998. № 2. Pp. 121–128. (in Russian).

2. Leont'ev, N.E. Osnovy teorii fil'tratsii: Uchebnoe posobie [Filtration fundamentals]. Moscow, 2009. 88 p. (in Russian).

3. Leibenzon, L.S. Dvizhenie prirodnykh zhidkostei i gazov v poristoi srede [Nature liquids and gases flow through porous medium]. Moscow, 1947. Pp. 11-24. (in Russian).

4. Basniev, K.S. Dmitriev, N.M., Rozenberg, G.D. Neftegazovaia gidromekhanika [Oil and gas hydromechanics]. Moscow, 2005. Pp. 376-380. (in Russian).

5. Kheifets, L.I., Neimark, A.V. Mnogofaznye protsessy v poristykh sredakh [Multiphase processes in porous medium]. Moscow, 1982. Pp. 29-33. (in Russian).

6. Shvidler, M.I. Statisticheskaia gidrodinamika poristykh sred [Statistical hydromechanics of porous medium]. Moscow: Nedra, 1985. 288 p. (in Russian).

7. Shvidler, M.I. Fil'tratsionnye techeniia v neodnorodnykh sredakh [Filtration flows in heterogeneous medium]. Moscow, 1963. 136 p. (in Russian).

8. Slichter, С.S. Part II of the 19th Annual Report of the United States Geological Survey,

1898. 295 p.

9. Romm, E.S. Strukturnye modeli porovogo prostranstva gornykh porod [Structural models of porous medium of rock formations]. Leningrad, 1985. 240 p. (in Russian).

10. Masket, M. Techenie odnorodnykh zhidkostei v poristoi srede [The flow of homogeneous fluids through porous medium] / Transl. fr. Eng. Moscow — Izhevsk, 2006. 640 p. (in Russian).