Absolute Permeability Tensors of Digital Models of Porous Media Under Various Boundary Conditions And Driving Forces

• Published in: Journal of engineering physics and thermophysics 2023, Vol.96 (1), p.39-49
• Main Authors: Zakirov, T. R., Khramchenkov, M. G.
• Format: Article
• Language: English
• Subjects: Analysis; Anisotropic media; Anisotropy; Boundary conditions; Classical Mechanics; Complex Systems; Driving conditions; Engineering; Engineering Thermodynamics; External pressure; Filtration; Fluid flow; Heat and Mass Transfer; Incompressible flow; Incompressible fluids; Industrial Chemistry/Chemical Engineering; Liquid flow; Mathematical analysis; Mathematical models; Numerical analysis; Permeability; Porous media; Simulation methods; Tensors; Thermodynamics
• ISSN: 1062-0125; 1573-871X
• DOI: 10.1007/s10891-023-02659-3

For the first time, a systematic investigation has been made into the influence of external boundary conditions and driving forces of liquid flows in anisotropic porous media on their absolute permeability tensor. The investigations have been perfumed on the basis of numerical simulation of a one-phase flow of an incompressible fluid in a porous space using lattice Boltzmann equations. Consideration has been given to cases when anisotropic porous media have permeability tensors with zero and nonzero nondiagonal components. It has been shown that in the case when a porous medium has a permeability with zero nondiagonal components, and external boundary conditions do not exert a substantial influence on the coefficient of medium permeability measured in the presence of a pressure difference or a bulk force in it. In testing anisotropic porous media having a permeability tensor with nonzero nondiagonal components, the external boundary conditions influenced significantly the filtration characteristics of a medium. It has been established that periodic boundary conditions significantly reduce the sensitivity of filtration characteristics of an anisotropic medium to the type of a driving force compared to nonpermeable external boundary conditions. Anisotropic medium permeability tensors measured at the applied pressure difference are nonsymmetrical in both types of external boundary conditions. It has been found that the permeability tensors of such a medium are symmetrical only under periodic external conditions and in the presence of a driving bulk force.