Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks

Toms, Julianna; Müller, Tobias M.; Číž, Radim; Gurevich, Boris

doi:10.1016/j.soildyn.2006.01.008

Cited by 94 publications

(70 citation statements)

References 79 publications

(148 reference statements)

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“…The word "mesoscopic" refers to the size of inhomogeneities being much larger than the typical grain size but much smaller than the wavelength of the pulse. For instance, if there are mesoscopic patches of gas in a brine-saturated sandstone, diffusion of pore fluid between the patches dissipates the energy through conversion into the diffusive slow mode (White, 1975;Norris, 1993;Johnson, 2001;Toms et al, 2006). The mesoscopic flow mechanism can be modeled using Biot's equations of poroelasticity with spatially varying coefficients (e.g., Rubino et al, 2007;Masson and Pride, 2007).…”

Section: Introductionmentioning

confidence: 99%

Differential form and numerical implementation of Biot’s poroelasticity equations with squirt dissipation

Carcione

Gurevich

2011

GEOPHYSICS

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The squirt-flow wave attenuation mechanism is implemented in Biot's theory of poroelasticity in the form of differential equations. All the stiffnesses involved in the stress-strain relation become complex and frequency dependent, which can exactly be expressed in terms of kernels based on the Zener mechanical model. In the time domain, this approach implies time convolutions, which are circumvented by introducing memory variables. The differential equations are consistent with Gassmann's and Mavko-Jizba equations at low and high frequencies, respectively. All the coefficients in the poro-viscoelastic differential equations have a clear physical meaning and can be obtained or estimated from independent measurements. The key additional parameters are the dry-rock bulk modulus at a confining pressure where all the compliant pores are closed, i.e., a hypothetical rock without the soft porosity, the grain-contact aspect ratio and the compliant porosity. We recasted the wave equation in the particle-velocity/stress formulation and solved it by using a time-splitting technique and the Fourier pseudospectral method to compute the spatial derivatives. The algorithm can be used to obtain synthetic wave fields in inhomogeneous media.

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Section: Introductionmentioning

confidence: 99%

Differential form and numerical implementation of Biot’s poroelasticity equations with squirt dissipation

Carcione

Gurevich

2011

GEOPHYSICS

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“…Since then, significant progress has been made by considering various patch distributions and flow regimes Odé, 1979a, 1979b;Norris, 1993;Gelinsky et al, 1998;Johnson, 2001;Gurevich, 2004, 2005;Müller et al, 2008;Gurevich et al, 2009;Picotti et al, 2010͒. More references for this topic are found in Toms et al ͑2006͒. When a gas pocket is subjected to the macroscopic pressure field of a compressional seismic wave ͑i.e., on a length scale much larger than the size of the inhomogeneity͒, the pocket will contract and expand.…”

Section: Introductionmentioning

confidence: 99%

Exact expression for the effective acoustics of patchy-saturated rocks

2010

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Seismic effects of a partially gas-saturated subsurface have been known for many years. For example, patches of nonuniform saturation occur at the gas-oil and gas-water contacts in hydrocarbon reservoirs. Open-pore boundary conditions are applied to the quasi-static Biot equations of poroelasticity to derive an exact analytic expression of the effective bulk modulus for partially saturated media with spherical gas patches larger than the typical pore size. The pore fluid and the rock properties can have different values in the central sphere and in the surrounding region. An analytic solution prevents loss of accuracy from ill-conditioned equations as encountered in the numerical solution for certain input. For a sandstone saturated with gas and water, we found that the P-wave velocity and attenuation in conventional models differ as much as 15% from the exact solution at seismic frequencies. This makes the use of present exact theory necessary to describe patchy saturation, although ͑more realistic͒ complex patch shapes and distributions were not considered. We found that, despite earlier corrections, the White conventional model does not yield the correct low-frequency asymptote for the attenuation.

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“…Toms et al [2006] give a review of different models. Two important features of wave-induced flow in porous media with partial saturation is the effective isotropy of the bulk medium and the absence of shear wave attenuation, which facilitates the theoretical analysis.…”

Section: Discussionmentioning

confidence: 99%

Anisotropic dispersion and attenuation due to wave‐induced fluid flow: Quasi‐static finite element modeling in poroelastic solids

Wenzlau¹,

Altmann²,

Müller³

2010

J. Geophys. Res.

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[1] Heterogeneous porous media such as hydrocarbon reservoir rocks are effectively described as anisotropic viscoelastic solids. They show characteristic velocity dispersion and attenuation of seismic waves within a broad frequency band, and an explanation for this observation is the mechanism of wave-induced pore fluid flow. Various theoretical models quantify dispersion and attenuation of normal incident compressional waves in finely layered porous media. Similar models of shear wave attenuation are not known, nor do general theories exist to predict wave-induced fluid flow effects in media with a more complex distribution of medium heterogeneities. By using finite element simulations of poroelastic relaxation, the total frequency-dependent complex stiffness tensor can be computed for a porous medium with arbitrary internal heterogeneity. From the stiffness tensor, velocity dispersion and frequency-dependent attenuation are derived for compressional and shear waves as a function of the angle of incidence. We apply our approach to the case of layered media and to that of an ellipsoidal poroelastic inclusion. In the case of the ellipsoidal inclusion, compressional and shear wave modes show significant attenuation, and the characteristic frequency dependence of the effect is governed by the spatiotemporal scale of the pore fluid pressure relaxation. In our anisotropic examples, the angle dependence of the attenuation is stronger than that of the velocity dispersion. It becomes clear that the spatial attenuation patterns show specific characteristics of waveinduced fluid flow, implying that anisotropic attenuation measurements may contribute to the inversion of fluid transport properties in heterogeneous porous media.Citation: Wenzlau, F., J. B. Altmann, and T. M. Müller (2010), Anisotropic dispersion and attenuation due to wave-induced fluid flow: Quasi-static finite element modeling in poroelastic solids,

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Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks

Cited by 94 publications

References 79 publications

Differential form and numerical implementation of Biot’s poroelasticity equations with squirt dissipation

Differential form and numerical implementation of Biot’s poroelasticity equations with squirt dissipation

Exact expression for the effective acoustics of patchy-saturated rocks

Anisotropic dispersion and attenuation due to wave‐induced fluid flow: Quasi‐static finite element modeling in poroelastic solids

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