ABSOLUTE PERMEABILITY TENSORS OF DIGITAL MODELS OF POROUS MEDIA UNDER VARIOUS BOUNDARY CONDITIONS AND DRIVING FORCES

For the first time, a systematic investigation has been made into the infl uence 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.
   
Author:  T. R. Zakirov, M. G. Khramchenkov
Keywords:  permeability tensor, anisotropy, mathematical modeling, boundary conditions
Page:  39