Release:2015, Vol. 1. №1(1)
About the authors: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; email@example.com
Abstract:A porous medium, whose channels have a complex shape and are formed by regular structures, is considered in the article. The authors present a method to determine the permeability of a medium by direct hydrodynamic modeling. The fluid rate is calculated by solving the system of Navier–Stokes equations in the amount of one pore. Then, with the help of Darcy’s law, the permeability of the porous medium is determined. Numerical implementation is carried out in conjunction of open software packages: SALOME–OpenFOAM–Paraview. The geometry of the pore space and the computational mesh are designed with the help of SALOME software package. The calculations are performed with the OpenFOAM package. Visualization of calculations is implemented in the package Paraview. Verification of the solver is carried out on the test case of Poiseuille flow. The article shows that the degree of overlapping spheres permeability decreases rapidly with the reduction of porosity. A close agreement between the results of calculations and analytical lower estimator for the permeability is given in the article by Igoshin D.E., Nikonova O.A., Mostovoy P.Ya. which is the first quoted in the paper.
1. Igoshin, D.E., Nikonova, O.A., Mostovoy, P.Ya. Simulation of the porous medium by regular packages of intersecting spheres // Tyumen State University Herald. 2014. №. 7. Pp. 34–42. (in Russian).
2. Romm, E.S. Structural models of porous medium of earth materials. Saint-Petersburg: Nedra, 1985. 240 p. (in Russian).
3. Leibenson, L.S. The flow of natural liquids and gases through porous medium. Moscow, 1947. Pp. 11–24. (in Russian).
4. Heifets, L.I., Neimark, A.V. Multiphase processes in porous medium. Moscow: Himiya, 1982. Pp. 29–33. (in Russian).
5. Schwindler, M.I. Statistical hydromechanics of porous medium. Moscow: Nedra, 1985. 288 p. (in Russian).
6. Darcy Henry Les fontaines publiques de la ville de Dijon: exposition et application des principes à suivre et des formules à employer dans les questions de distribution d'eau... Paris: V. Dalmont, 1856. 647 p.
7. Basniev, K.S., Kochina N.I. Underground fluid mechanics. Moscow: Nedra, 1993. 416 p. (in Russian).
8. Leontyev, N.E. Filtration fundamentals. Moscow: MSU, 2009. 88 p. (in Russian).
9. Bourbie, Т., Coussy, O., Zinszner, B. Acoistique des Milieux Poreux. Chap. 1. Paris: Technip, 1986.
10. Wong, P.Z., Koplik, J., Tomanic, J.P. // Phys. Rev. Ser. B. 1984. Vol. 30. P. 6606.
11. Guoyn, Е., Oger, L., Fiona, T.J. // J. Phys. Ser. D. 1987. Vol. 20. P. 1637.