Wave propagation in single- and double-porosity deformable porous media saturated by multiphase fluids

The volume averaging technique is used to derive the macroscopic constitutive relations, mass and momentum balance equations for fractured and nonfractured porous media saturated by two immiscible Newtonian fluids. The solid grains and matrix are assumed to be linearly elastic and deformations are assumed to be small. The final sets of equations are limited to low frequencies. In the first part of the study, the governing equations for both quasi-static and dynamics of porous media saturated by two fluids are obtained. An analytical solution is obtained for the quasi-static case. Body waves in an infinite porous medium are investigated. An additional compressional wave which is associated with the pressure difference between the fluid phases is demonstrated. The phase velocities and attenuation coefficients of body waves are examined for material properties characterizing sandstone saturated by air and water phases. In the second part of the study, dynamics of fractured porous media saturated by two fluids is investigated based on the double-porosity representation. An effective stress expression is derived for saturated fractured porous media. Body waves are investigated and an additional compressional wave associated with the fluid phase in the fractures is shown. The effects of fractures, saturation, frequency are numerically examined for material parameters characterizing a fractured sandstone saturated by air and water phases.