Abstract:Based on the mechanics of fluids in porous media and the continuum mechanics,a continuum theory of multiphase porous media is developed to analyze the propagation of elastic waves in a porous medium saturated by a mixture of two immiscible,viscous,compressible fluids. The behavior of porous media can be described by three equations of motion,two continuity equations of flow,and a supplementary equation that describes the constitutive relationships. A closed-form solution is derived for a fully coupled model considering the capillary pressure and irreducible/residual saturation,which demonstrates the existence of three types of compressional waves and one type of shear wave. The theoretical results are plotted and compared with the experimental data available in the previous studies. This solution is highly versatile in that it considers compression of the solid grain,compression of both pore fluids,deformation of the porous skeleton,and spatial damping. In addition,all the material parameters in this model are measurable.