Biot Theory for Porous Media

We have studied the propagation of 12 MHz transverse ultrasonic waves in a porous ceramic containing liquid 4He. Both the sound velocity and the attenuation clearly show the superfluid nature of helium. The helium in the pores increases the system's effective density by an amount proportional to the normal-fluid density and so decreases the sound speed. The decoupling of the superfluid fraction below the lambda transition allows us to use the shear wave essentially as a "high-frequency torsional oscillator" to determine the superfluid density and pore tortuosity. The sound attenuation in this system is due to the same mechanism as for fourth sound, namely, viscous losses due to motion of the normal-fluid component. We observed an attenuation proportional to the normal-fluid density and compare this result to predictions of the Biot theory of sound propagation in fluid-filled porous media.

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Acoustic phenomena in porous media studied by transient grating spectroscopy: a critical test of the Biot theory

The Journal of the Acoustical Society of America ◽

10.1121/1.2933184 ◽

2008 ◽

Vol 123 (5) ◽

pp. 3155-3155

Author(s):

Riccardo Cucini ◽

Andrea Taschin ◽

Paolo Bartolini ◽

Renato Torre

Keyword(s):

Porous Media ◽

Biot Theory ◽

Transient Grating ◽

Critical Test ◽

Transient Grating Spectroscopy ◽

Grating Spectroscopy

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Elastic waves in porous media saturated with non-wetting fluid

The APPEA Journal ◽

10.1071/aj19196 ◽

2020 ◽

Vol 60 (1) ◽

pp. 315

Author(s):

Jimmy X. Li ◽

Reza Rezaee ◽

Tobias M. Müller ◽

Mohammad Sarmadivaleh

Keyword(s):

Porous Media ◽

Apparent Viscosity ◽

Elastic Waves ◽

Solid Wall ◽

Seismic Exploration ◽

Solid Matrix ◽

Biot Theory ◽

Bulk Fluid ◽

Wave Induced ◽

Wetting Fluid

Elastic waves have widely been used as a non-destructive probing method in oilfield exploration and development, and the most well-known applications are in seismic exploration and borehole sonic logging. For waves in porous media, it is popular to use the Biot theory, which incorporates the wave-induced global flow, accounting for the frictional attenuation. The Biot theory assumes that the fluid is wetting to the solid matrix. However, the fluid is not always wetting the rock in real reservoirs. It was previously revealed that a non-wetting fluid parcel tends to slip on the solid wall pore boundary where the intermolecular potential between the fluid and solid wall is weaker than in wetting fluid conditions. This particular slippage feature means that the coupling relationship between the fluid and solid frame and frictional dissipation is likely to be very different between non-wetting and wetting fluid situations. We characterise this wave-induced slippage using an apparent viscosity for the non-wetting fluid within the thin viscous boundary layer. This apparent viscosity is smaller than the viscosity of the bulk fluid. We demonstrate that the slip correction affects the dynamic permeability and dynamic tortuosity and results in slippage/wettability dependent phase velocities and attenuation of the fully fluid-saturated rock.

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A Multi-Scale and Level Set Algorithm for the Inverse Problem of Wave Equation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.275-277.413 ◽

2013 ◽

Vol 275-277 ◽

pp. 413-416

Author(s):

Ying He ◽

Chun Yan He

Keyword(s):

Porous Media ◽

Elastic Wave ◽

Level Set ◽

Wave Equations ◽

Biot Theory ◽

Saturated Porous Media ◽

Parameter Recovery ◽

Multi Scale ◽

Elastic Wave Equations ◽

Fluid Saturated Porous Media

In this paper, we construct the multi-scale and level set algorithm of the parameter recovery for the elastic wave equations in the fluid-saturated porous media. Firstly, based on the Biot theory, we apply the multi-scale method to simulate the propagation of 2-D elastic wave in fluid-saturated porous media. Secondly, the level set method is introduced to the general parameter estimation problem.

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Research of Porous Solid - Fluid Interface Scholte Wave

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.538-541.2175 ◽

2012 ◽

Vol 538-541 ◽

pp. 2175-2180

Author(s):

Zu Feng Xie ◽

Qing Bang Han ◽

Chang Ping Zhu

Keyword(s):

Porous Media ◽

Function Method ◽

Sound Propagation ◽

Secular Equation ◽

Biot Theory ◽

Propagation Characteristics ◽

Fluid Interface ◽

Medium Interface ◽

Interface Wave ◽

Scholte Wave

This paper establishes the theoretical model of Scholte wave velocity on the fluid-porous medium interface based on the Biot theory of porous media. We firstly simulates and analysis sound propagation characteristics of fluid-saturated porous, and then we deduces the secular equation of fluid-solid interface wave on semi-infinite half-space applying potential function method. This study will provide a theoretical guidance of detecting the interface wave between fluid and porous media.

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