Two-Phase Computational Model for Wave Propagation in Deforming Saturated Porous Medium

The new two-phase model for a compressible fluid flow in deforming porous media is presented. The derivation of the model is based on the symmetric hyperbolic thermodynamically compatible systems theory, which is developed with the use of the first principles and fundamental laws of thermodynamics. The governing PDEs form the first order hyperbolic system and can be used for studying a wide variety of processes in saturated porous media, including small amplitude wave propagation. Our theory predicts the three types of waves: fast and slow pressure waves and a shear wave, as it is in Biot's model. The material constants of the model are fully determined by the properties of the solid and the fluid phases, and unlike Biot's model do not contain empirical parameters. The governing PDEs for small amplitude wave propagation in a saturated porous medium are presented, and the efficient numerical method has been developed for solving these PDEs, based on the finite difference staggered-grid scheme of fourth order spatial accuracy with modified coefficients to provide approximation in inhomogeneous media. An application of the developed computational framework to solving a series of test problems confirms the robustness and efficiency of the approach presented.