Wave equations for porous media described by the Biot model

Area of Science:

• Acoustics
• Geophysics
• Materials Science

Background:

• Previous models for acoustic waves in Biot poroelastic media were limited to low or high frequency asymptotic cases.
• Low-frequency models used integer-order loss terms, while high-frequency models used fractional-order terms.

Purpose of the Study:

• To develop a unified time-domain wave equation for all three Biot wave solutions across all frequencies.
• To incorporate dynamic permeability and squirt flow mechanisms into a single, physically based model.

Main Methods:

• Derived a time-domain partial differential equation from the Biot poroelastic material response function.
• Approximated compressional modes and dynamic permeability, representing the latter with a fractional pseudo-differential operator.
• Introduced optimal correction factors for dispersion and attenuation, and described squirt flow incorporation via the Extended Biot model.

Main Results:

• Proposed a novel wave equation valid for all frequencies and wave solutions in Biot media.
• The dynamic permeability is effectively modeled using a fractional pseudo-differential operator.
• The model incorporates squirt flow and satisfies the passivity criterion.

Conclusions:

• The developed wave equation provides a comprehensive representation of acoustic wave propagation in Biot poroelastic media.
• This unified approach overcomes the limitations of previous frequency-specific models.
• The model's physical basis and adherence to the passivity criterion enhance its reliability for geophysical and material science applications.