A model for wave propagation in a porous solid saturated by a three-phase fluid

Area of Science:

• Geophysics
• Poroelasticity
• Multiphase Flow

Background:

• Wave propagation in porous media is fundamental to geophysics.
• Existing models often simplify fluid saturation to single-phase systems.
• Understanding multiphase fluid interactions is key for accurate subsurface characterization.

Purpose of the Study:

• To develop a generalized model for wave propagation in poroelastic media saturated by three-phase fluids.
• To incorporate capillary effects between fluid phases using Lagrange multipliers.
• To extend Biot's theory to complex, multi-component fluid systems.

Main Methods:

• Utilized the principle of virtual complementary work with Lagrange multipliers for capillary relations.
• Derived constitutive relations, strain energy density, and generalized stresses/strains.
• Applied laminar flow assumptions and Darcy's law for three-phase flow.
• Performed plane wave analysis on the derived equations of motion.

Main Results:

• The model predicts the existence of four distinct compressional waves (Type I, II, III, IV) and one shear wave.
• Derived kinetic and dissipative energy density functions for the system.
• Numerical examples illustrate wave behavior dependence on fluid saturation and frequency.

Conclusions:

• The generalized model accurately describes wave propagation in three-phase fluid-saturated poroelastic media.
• The inclusion of capillary effects and multiphase flow is essential for realistic subsurface wave modeling.
• The predicted wave behaviors offer insights into seismic wave interactions in complex geological formations.