Wave propagation in fractured porous media saturated by two immiscible fluids

A study of wave propagation in fractured porous media saturated by two immiscible fluids is presented, based on the double-porosity concept. The macroscopic constitutive relations and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations, and assuming small deformations. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law in fractured porous media. In the simplest case, the final set of governing equations reduce to Blot's equations containing the same parameters as Blot and Willis. Then, we demonstrate the existence of four compressional waves and one rotational wave. The first and third compressional waves are analogous to the fast and slow compressional waves in Blot's theory. The second compressional wave arises because of fractures, whereas the fourth compressional wave is associated with the pressure difference between the fluid phases in the porous blocks. All compressional waves, except the first, are diffusive-type waves, i.e., highly attenuated and nonexistent at low frequencies.