Acoustic wave propagation in a porous medium saturated with two fluids and a solid

Wave propagation in multi-phase porous media is a significant research topic. There are a series of studies about porous media saturated with a single fluid, a solid and a fluid, two fluids, and three fluids. Some gas hydrate-bearing sediments are typical multiphase porous media saturated with a solid (gas hydrates) and two fluids (water and gas). Based on existing theories of porous media, we develop a theory and give a comprehensive analysis of wave propagation in a poroelastic medium saturated with two fluids and a solid. Initially, we establish the constitutive relations and equations of motion. Based on Biot's approach for describing the equations of motion in fluid-saturated porous media at the macroscale, the kinetic energy density, potential energy density, and dissipative energy density are derived. After deriving the equations of motion, a plane wave analysis predicts the existence of four compressional waves, denoted P1, P2, P3, and P4 waves, and two shear waves, denoted S1 and S2 waves. Numerical examples are presented to demonstrate how velocities and attenuations of various waves behave with gas saturation, gas hydrate saturation, and frequency. A model degradation to porous media saturated with a single fluid supports the validity of the theory, which enriches the theory of multiphase porous media and provides a foundation for the evaluation of gas hydrate-bearing sediments.