Two-phase hyperbolic model for porous media saturated with a viscous fluid and its application to wavefields simulation

TL;DR

This paper introduces a new hyperbolic two-phase model for porous media saturated with viscous fluids, capturing wave propagation and dissipation mechanisms, and demonstrates its application to wavefield simulations.

Contribution

It develops a novel hyperbolic two-phase model within the SHTC framework that incorporates viscosity and dissipative effects for porous media.

Findings

The model predicts three wave types: fast, slow, and shear waves.

Shear waves attenuate rapidly due to fluid viscosity.

Shear waves can be observed near interfaces with different porosity.

Abstract

We derive and study a new hyperbolic two-phase model of a porous deformable medium saturated by a viscous fluid. The governing equations of the model are derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems and by generalizing the unified hyperbolic model of continuum fluid and solid mechanics. Similarly to the unified model, the presented model takes into account the viscosity of the saturating fluid through a hyperbolic reformulation. The model accounts for such dissipative mechanisms as interfacial friction and viscous dissipation of the saturated fluid. Using the presented nonlinear finite-strain SHTC model, the governing equations for the propagation of small-amplitude waves in a porous medium saturated with a viscous fluid are derived. As in the conventional Biot theory of porous media, three types of waves can be found: fast and slow compression waves and shear waves. It turns out that the shear wave attenuates rapidly due to the viscosity of the saturating fluid, and this wave is difficult to see in typical test cases. However, some test cases are presented in which shear waves can be observed in the vicinity of interfaces between regions with different porosity.