Elastic wave attenuation and dispersion induced by mesoscopic flow in double-porosity rocks

Zheng, Pei; Ding, B.Z.; Sun, Xiuting

doi:10.1016/j.ijrmms.2016.11.018

Cited by 25 publications

(13 citation statements)

References 31 publications

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“…It is noted that there is no general arithmetic or algebraic method for finding the roots of such equations except in the case of a cubic equation with real coefficients, which roots can be obtained using Cardan's formula. So numerical root finder must be resorted to, and thus, Newton's iteration algorithm will be used to solve the characteristic equation for the complex roots λ 2 (for further details, see ).…”

Section: Analytical Solutions Of One‐dimensional Problemsmentioning

confidence: 99%

One-dimensional analytical solution for mesoscopic flow induced damping in a double-porosity dual-permeability material

Zheng

Cheng

2017

Int. J. Numer. Anal. Meth. Geomech.

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Heterogeneities, such as fractures and cracks, are ubiquitous in porous rocks. Mesoscopic heterogeneities, that is, heterogeneities on length scales much larger than typical pore size but much smaller than the wavelength, are increasingly believed to be responsible for significant wave energy loss in the seismic frequency band. When a compressional wave stresses a material containing mesoscopic heterogeneities, the more compliant parts of the material (e.g., fractures and cracks) respond with a greater fluid pressure than the stiffer portions (e.g., matrix pores). The induced fluid flow, resulting from the pressure gradients developed on such scale, is called mesoscopic flow. In the present study, the double-porosity dual-permeability model is adopted to incorporate mesoscopic heterogeneities into rock models to account for the attenuation of wave energy. Based on the model, the damping effect due to mesoscopic flow in a one-dimensional porous structure is investigated. Analytical solutions for several boundary-value problems are obtained in the frequency domain. The dynamic responses of infinite and finite porous layer are examined. Numerical calculations show that the damping effect of mesoscopic flow is significant on the pore pressure response and the resulting effective stress. For the displacement, the effect is seen only at the very low frequency range or near the resonance frequencies.

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Section: Analytical Solutions Of One‐dimensional Problemsmentioning

confidence: 99%

One-dimensional analytical solution for mesoscopic flow induced damping in a double-porosity dual-permeability material

Zheng

Cheng

2017

Int. J. Numer. Anal. Meth. Geomech.

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“…In the last decades, wave dispersion and attenuation in natural reservoir rocks attract more and more attentions (Dutta and Ode, 1979, Norris, 1993, Dvorkin et al, 1995, Sams et al, 1997, Berryman and Wang, 2000, Johnson, 2001, Pride et al, 2004, Berryman and Pride, 2005, Carcione and Picotti, 2006, Toms et al, 2006, Rubino and Holliger, 2012, Sharma, 2017, Zheng et al, 2017. Intrinsic attenuation is believed mainly come from fluid flow in saturated rocks, which is driven by pressure gradient through 'Darcy's law'.…”

Section: Introductionmentioning

confidence: 99%

On the theory of Biot-patchy-squirt mechanism for wave propagation in partially saturated double-porosity medium

Sun

2021

Physics of Fluids

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Reservoir rocks are usually composed of a coherent heterogeneous porous matrix saturated by multiple fluids. At long wavelength limit, the composite material of solid skeleton is usually regarded as homogeneous media. However, at grain scale or high loading rate, non-uniform fluid flow at internal interface of heterogeneity plays essential role in wave dispersion and attenuation. Formulating wave propagation in partially saturated and fractured rocks is challenging and of great interests in geoscience. Here we raise a Biot-patchy-squirt (BIPS) model to characterize wave dispersion/attenuation in fractured poroelastic media saturated by two immiscible fluids. BIPS model incorporates the mechanism of local fluid-interface flow (LFIF) and squirt flow into global fluid flow simultaneously. Theoretical analysis show that wave attenuations caused by viscous dissipation, squirt flow and patchy interface vibration are distinct from each other. BIPS is intrinsically consistent with Biot theory, squirt and LFIF model and reduces to such mechanism in limiting conditions. More interestingly, numerical results show that coupling between LFIF and squirt flow is of evident importance to P-wave dispersion and attenuation. Comparisons with experimental data indicate that BIPS model is computationally reliable and in reasonably good agreement with experimental data. This study advance our understanding of the fundamental physics of wave propagation in natural reservoir rocks and push forward the potential applications of the triple dispersion/attenuation mechanism to wave velocity estimation in deep earth.

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“…The phenomenological equations of the TLP model are proposed on the basis of Biot's theory. Zheng et al (2017) investigated the wave attenuation and phase velocity dispersion induced by wave-induced mesoscopic fluid flow on the basis of doubleporosity, dual-permeability theory.…”

Section: Introductionmentioning

confidence: 99%

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

2019

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Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves (i.e., incident and reflected) in an elastic medium are considered as homogeneous (i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous (i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

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Elastic wave attenuation and dispersion induced by mesoscopic flow in double-porosity rocks

Cited by 25 publications

References 31 publications

One-dimensional analytical solution for mesoscopic flow induced damping in a double-porosity dual-permeability material

One-dimensional analytical solution for mesoscopic flow induced damping in a double-porosity dual-permeability material

On the theory of Biot-patchy-squirt mechanism for wave propagation in partially saturated double-porosity medium

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

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