Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model)—Part I: Biot theory

Dutta, N. C.; Odé, H.

doi:10.1190/1.1440938

Cited by 349 publications

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“…The fluid displacement field w(z) (Plate 2) shows that the pore fluid flows toward the surface at low frequencies (thus equilibrating pressure) and at high frequencies there is no fluid displacement (since the timescale for pressure diffusion is longer than the period of the wave) and thus there is no pore pressure equilibrium. The low frequency region is often referred to as "relaxed" state of the pore fluid and the high frequency region is "unrelaxed" state [Mavko et al 1998, Dutta and Ode, 1979a, 1979b.…”

Section: Discussionmentioning

confidence: 99%

Liquefaction and dynamic poroelasticity in soft sediments

Bachrach¹,

Nur²,

Agnon³

2001

J. Geophys. Res.

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Abstract. In this paper we present a model that can explain earthquake-induced dynamic liquefaction in unconsolidated sediments without the need for irreversible compaction. We study the behavior of a poroelastic layer subjected to a periodic cyclic stress using dynamic poroelasticity formulation. We show that in such a layer pore pressure may increase due to a resonant mode of Biot's type II wave, an attenuated mode whose wavelength is short and can resonate inside a layer of few meters thickness. We show that in sediments such as sand, where the shear modulus is less than 0.3 GPa, pore pressure can exceed the total stress. This will cause unconsolidated material to liquefy. We also show that as the elastic coefficient of the sediment decreases, the pore pressure induced by B iot's type II wave increases. Thus, in a material where the elastic moduli are pressure dependent (e.g., Hertzian material) the increased pore pressure reduces the stiffness and thus liquefaction is more likely to occur.

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Section: Discussionmentioning

confidence: 99%

Liquefaction and dynamic poroelasticity in soft sediments

Bachrach¹,

Nur²,

Agnon³

2001

J. Geophys. Res.

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“…In this section, we demonstrate that under the assumptions formulated in Section 2 equations (6), (12), and (20) can be reduced to the system of equations obtained by Biot [8,10], see also [15]. At the same time, neglecting the inertial terms in these equations, leads to the pressure diffusion equation used in hydrology and petroleum engineering for well test analysis, see [42,24] or books [28,4].…”

Section: Relationship To Biot's Poroelasticity and Pressure Diffusionmentioning

confidence: 99%

Low-Frequency Asymptotic Analysis of Seismic Reflection from a Fluid-Saturated Medium

et al. 2006

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Abstract. A low-frequency asymptotic representation of the reflection of seismic signal from a fluid-saturated porous medium has been obtained.First, derivation of the main equations of the theory of poroelasticity and the pressure diffusion equation, which is routinely used in well-test analysis, has been reviewed. It has been observed that both models can be derived from the basic principles of filtration theory. In addition, Biot's tortuosity parameter has been related to the relaxation time in the dynamic Darcy's law.Second, the reflection of a low-frequency signal from a plane interface between elastic and elastic fluid-saturated porous media has been studied. An asymptotic scaling of the frequency-dependent component of the reflection coefficient has been obtained. Namely, it has been established that this component is asymptotically proportional to the square root of the product of the reservoir fluid mobility and the frequency of the signal. The dependence of this scaling on the dynamic Darcy's low relaxation time and the Biot's tortuosity factor has been investigated as well.

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“…In this section, we demonstrate that under the assumptions formulated in Section 2 equations (6), (11), and (19) can be reduced to the system of equations obtained by Biot [7,9], see also [14]. At the same time, neglecting the inertial terms in these equations, leads to the pressure diffusion equation used in hydrology and petroleum engineering for well test analysis, see [25,3].…”

Section: Relationship To Biot's Poroelasticity and Pressure Diffusionmentioning

confidence: 99%

“…Further comparison between the elastic coefficients reveals that under the assumptions (20) the coefficient γ in the notations of [14] is equal to one and the other coefficients are, respectively, equal…”

Section: Relationship To Biot's Poroelasticity and Pressure Diffusionmentioning

confidence: 99%

A hydrologic view on Biot's theory of poroelasticity

Silin¹,

Korneev²,

Goloshubin³

et al. 2004

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Abstract. The main objective of this work is to obtain a simplified asymptotic representation of the reflection of seismic signal from a fluid-saturated porous medium in the low-frequency domain.In the first part, we derive the equations of low-frequency harmonic waves in a fluid-saturated elastic porous medium from the basic concepts of filtration theory. We demonstrate that the obtained equations can be related to the poroelasticity model of Frenkel-Gassmann-Biot, and to pressure diffusion model routinely used in well test analysis as well. We thus try to put the poroelastic and filtration theories on the same ground.We study the reflection of a low-frequency signal from a plane interface between elastic and elastic fluid-saturated porous media. We obtain an asymptotic scaling of the frequency-dependent component of the reflection coefficient with respect to a dimensionless parameter depending on the frequency of the signal and the reservoir fluid mobility. We also investigate the impact of the relaxation time and tortuosity on this scaling.

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Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model)—Part I: Biot theory

Cited by 349 publications

References 0 publications

Liquefaction and dynamic poroelasticity in soft sediments

Liquefaction and dynamic poroelasticity in soft sediments

Low-Frequency Asymptotic Analysis of Seismic Reflection from a Fluid-Saturated Medium

A hydrologic view on Biot's theory of poroelasticity

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