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A two-phase model and its application to wavefields numerical simulation arediscussed in the context of modeling of compressible fluid flows in elasticporous media. The derivation of the model is based on a theory ofthermodynamically compatible systems and on a model of nonlinearelastoplasticity combined with a two-phase compressible fluid flow model. Thegoverning equations of the model include phase mass conservation laws, a totalmomentum conservation law, an equation for the relative velocities of thephases, an equation for mixture distortion, and a balance equation forporosity. They form a hyperbolic system of conservation equations that satisfythe fundamental laws of thermodynamics. Two types of phase interaction areintroduced in the model: phase pressure relaxation to a common value andinterfacial friction. Inelastic deformations also can be accounted for bysource terms in the equation for distortion. The thus formulated model can beused for studying general compressible fluid flows in a deformableelastoplastic porous medium, and for modeling wave propagation in a saturatedporous medium. Governing equations for small-amplitude wave propagation in auniform porous medium saturated with a single fluid are derived. They form afirst-order hyperbolic PDE system written in terms of stress and velocitiesand, like in Biot's model, predict three types of waves existing in realfluid-saturated porous media: fast and slow longitudinal waves and shear waves.For the numerical solution of these equations, an efficient numerical methodbased on a staggered-grid finite difference scheme is used. The results ofsolving some numerical test problems are presented and discussed

Modeling wavefields in saturated elastic porous media based on thermodynamically compatible system theory for multiphase mixtures