Computation of the biot drag and virtual mass coefficients

Abstract

The Biot equations model the propagation of acoustic waves in fluid-saturated porous media. The equations contain coefficients which depend upon the frequency and the fabric, or microstructure, of the solid constituent. Recently, a method has been developed for determining the drag and virtual mass coefficients in Biot's equations as functions of frequency. The method requires solving for the motion of the fluid in the pores when the pore walls are subjected to a spatially uniform, oscillatory motion. To determine the fluid motion in realistic pore spaces, a numerical method must be used. In this paper the finite element method is used to determine the fluid motion. The drag and virtual mass coefficients are determined for several two-dimensional pore spaces. It is concluded that the drag coefficient is very insensitive to the pore geometry, while the virtual mass coefficient is sensitive to the pore geometry. It is also shown that the results can be expressed in nondimensional forms which permit the coefficients to be determined for different values of a characteristic linear dimension of the pore space.