  A two-phase model and its application to wavefields numerical simulation are
discussed in the context of modeling of compressible fluid flows in elastic
porous media. The derivation of the model is based on a theory of
thermodynamically compatible systems and on a model of nonlinear
elastoplasticity combined with a two-phase compressible fluid flow model. The
governing equations of the model include phase mass conservation laws, a total
momentum conservation law, an equation for the relative velocities of the
phases, an equation for mixture distortion, and a balance equation for
porosity. They form a hyperbolic system of conservation equations that satisfy
the fundamental laws of thermodynamics. Two types of phase interaction are
introduced in the model: phase pressure relaxation to a common value and
interfacial friction. Inelastic deformations also can be accounted for by
source terms in the equation for distortion. The thus formulated model can be
used for studying general compressible fluid flows in a deformable
elastoplastic porous medium, and for modeling wave propagation in a saturated
porous medium. Governing equations for small-amplitude wave propagation in a
uniform porous medium saturated with a single fluid are derived. They form a
first-order hyperbolic PDE system written in terms of stress and velocities
and, like in Biot's model, predict three types of waves existing in real
fluid-saturated porous media: fast and slow longitudinal waves and shear waves.
For the numerical solution of these equations, an efficient numerical method
based on a staggered-grid finite difference scheme is used. The results of
solving some numerical test problems are presented and discussed
