Calculation of Hydraulic Conductivity for a Porous Medium with Staggered Array of Solid Grains - 20087
For a porous medium with periodic array of solid grains. the flow of an incompressible viscous fluid in the pore space is considered with an aim of calculating the permeability of the medium. The solid grains are of ellipsoidal shape. For this purpose, a unit-cell boundary-value problem (Stokes problem) is solved numerically. With the assumption of periodicity of the medium structure and the fluid properties (in fact constant), the flow field and pressure distributions are determined numerically with inertial effects ignored. By applying the theory of homogenization to the viscous flow through pore space, a microscale boundary-value problem is defined. After solving the problem, the permeability is determined by taking the micro-cell average of the velocity components, Various porous structures are chosen to allow a wide range of porosity values. The permeability increases mildly for porosity values in the lower range. But it increases sharply for porosity values in the upper range of the porosity. The permeability of the present study agrees with the Kozeny-Carman relation excellently for smaller porosity. Certain discrepancy between the calculated permeability in this study and the Kozeny-Carman relation appears and increases with porosity for larger porosity. It is believed that the discrepancy is due to the replacement of the pores by a bundle of capillaries, which is unrealistic, in the Kozeny-Carman relation. (authors)