One‐dimensional random patchy saturation model for velocity and attenuation in porous rocks

Müller, Tobias M.; Gurevich, Boris

doi:10.1190/1.1801934

Cited by 102 publications

(69 citation statements)

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“…For a random system of poroelastic layers where only the pore fluid properties spatially vary (according to an exponential autocorrelation function), Müller and Gurevich [3] obtained the frequency-dependent P-wave modulus:…”

Section: Wave-induced Flow In Partially Saturated Rocksmentioning

confidence: 99%

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A model for strong attenuation and dispersion of seismic P-waves in a partially saturated fractured reservoir

Brajanovski

Müller

Parra

2010

Sci. China Phys. Mech. Astron.

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In this work we interpret the data showing unusually strong velocity dispersion of P-waves (up to 30%) and attenuation in a relatively narrow frequency range. The cross-hole and VSP data were measured in a reservoir, which is in the porous zone of the Silurian Kankakee Limestone Formation formed by vertical fractures within a porous matrix saturated by oil, and gas patches. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interfaces between different types of inclusions (fractures, fluid patches) and background. Other models of intrinsic attenuation (in particular squirt flow models) cannot explain the amount of observed dispersion when using realistic rock properties. In order to interpret data in a satisfactory way we develop a superposition model for fractured porous rocks accounting also for the patchy saturation effect. attenuation, dispersion, Biot's slow wave, poroelasticity, fractures, patchy-saturation PACS: 43.35.Cg, 91.30.Ab, 91.30.Cd, 91.60.QrOne of the main intrinsic seismic wave dissipation mechanisms is associated with the wave-induced flow of the pore fluid. This effect occurs in a heterogeneous porous medium when a passing wave induces a local pore pressure gradient on the interface between the inclusion and the background. In order to equilibrate pressure, viscous fluid moves across the interface. The magnitude of induced pore-pressure as a function of loading stress (incident wave) depends on bulk moduli of fluid, grains and matrix (dry skeleton) respectively, P-wave velocity modulus of the matrix and porosity (all these parameters are included in proportionality factor between fluid pressure and total stress called "material parameter" [1] usually denoted by R). Whichever parameter changes in inhomogeneities, a pressure gradient will be induced and we get, in principle, the same attenuation effect.In geologically realistic structures the contrast of length scales and elastic properties between inclusions and background material might be very large. One such scenario occurs in the patchy-saturation model [2,3] describing fluid-saturated porous rocks having patches of different fluid (gas). In this case the main cause of induced pore pressure gradient is the difference in bulk moduli of fluids. According to Norris [1]: "The general mechanism does not assume partial saturation, but only that the medium is inhomogeneous. For example, the pores could be completely saturated with liquid but the compressibility of the solid frame may vary with position. However, the diffusion is greater if the fluid compressibility varies significantly from point to point". The other scenario occurs in the fractured rock model, where the main cause of induced pore pressure gradient is the difference in elastic moduli of rock matrix in the background and in the fractures [4][5][6]. In all these studies similar behavior of attenuation versus frequency is observed. In fact, we can say that the overall attenuation is a result of the interference of two pairs of Biot's [7] slow wave...

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Section: Wave-induced Flow In Partially Saturated Rocksmentioning

confidence: 99%

“…One such scenario occurs in the patchy-saturation model [2,3] describing fluid-saturated porous rocks having patches of different fluid (gas). In this case the main cause of induced pore pressure gradient is the difference in bulk moduli of fluids.…”

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confidence: 99%

A model for strong attenuation and dispersion of seismic P-waves in a partially saturated fractured reservoir

Brajanovski

Müller

Parra

2010

Sci. China Phys. Mech. Astron.

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“…Constitutive relations (45), (47), (48), (50), (54), (57), (62), (64), (69), (73), formulated in this section, together with the balance Eqs. (24) and ( describing mechanical properties of the fluid constituents in the unsaturated porous material and their interactions.…”

Section: Constitutive Relations For Stresses and The Interaction Forcesmentioning

confidence: 99%

“…These include, for example, porosimetry [20,21,69,70] and engineering of porous materials [1,42], groundwater flow [57,73], hydraulic engineering, oil and gas mining [3], geophysics [54,56] and drying processes [41,53]. It enables a thorough understanding and prediction of the course of phenomena in such materials, and consequently also, for example, determination of precise material characteristics, effective control of transport processes, and production of porous materials with desired physical properties.…”

Section: Introductionmentioning

confidence: 99%

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

Cieszko

2016

Meccanica

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A new macroscopic description of capillary transport of liquid and gas in porous materials is presented within the framework of multiphase continuum mechanics. It is assumed that unsaturated porous material form a macroscopic continuum composed of three constituents: gas, mobile liquid and capillary liquid, while the skeleton is rigid with an isotropic pore space structure. The capillary liquid forms a thin layer on the internal contact surface with the skeleton, is immoveable and contains the whole capillary energy. The remaining part of the liquid, surrounded by the layer of the capillary liquid and menisci, forms the constituent called mobile liquid. Both liquids exchange mass, momentum and energy in the vicinity of menisci surfaces during their motion, which is described by an additional macroscopic velocity field. A macroscopic scalar quantity is introduced, parametrizing changes of saturations, which for quasi static and stationary processes is equal to the capillary pressure. This quantity extends the dimensionality of the description of mechanical processes taking place in unsaturated porous materials. For the three fluid constituents of the medium, balance equations of mass and linear momentum and evolution equations for saturations are formulated. The constitutive relations for quantities describing mechanical processes in such a medium are proposed based on the dissipation inequality of mechanical energy for the whole system. A new approach is proposed, similar to that used in rational thermodynamics, based on entropy inequality analysis and the Lagrange multipliers method.

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“…[6] Müller and Gurevich [2004] are the first authors to account for randomness in the spatial distribution of the fluids. They do so using a 1-D approximation for the coherent wavefield in a random porous media and assuming a continuous random media with a distribution of different patch sizes.…”

Section: Introductionmentioning

confidence: 99%

Seismic attenuation due to patchy saturation

Masson

Pride

2011

J. Geophys. Res.

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[1] In porous rocks saturated in patches by two immiscible fluids, seismic compression causes the fluid with the larger bulk modulus to respond with a larger change in fluid pressure than the fluid with the smaller bulk modulus which results in fluid movement and seismic attenuation. For virtual rock samples having fluid distributions obtained using the invasion percolation model, attenuation is determined using finite difference numerical experiments based on the laws of poroelasticity. Analytical models are also proposed to explain the numerical results. When oil invades water, the equilibration is controlled by the geometry of the invading oil which has a narrow range of small diffusion lengths resulting in a single relaxation frequency at high frequencies and not much seismic band attenuation. When water invades oil, the defending oil controls the equilibration, and a power law emerges for how attenuation varies with frequency due to the fractal nature of how saturation is varying with scale in the defending oil. For air invading water, the geometry of the defending water controls the equilibration, and a large amount of attenuation is observed over a wide range of frequencies including the seismic band due to the wide range in water patch sizes. However, when water invades air, the narrow fingers of invading water control the equilibration, and there is a single relaxation frequency at high frequencies that does not result in much seismic band attenuation.

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One‐dimensional random patchy saturation model for velocity and attenuation in porous rocks

Cited by 102 publications

References 21 publications

A model for strong attenuation and dispersion of seismic P-waves in a partially saturated fractured reservoir

A model for strong attenuation and dispersion of seismic P-waves in a partially saturated fractured reservoir

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

Seismic attenuation due to patchy saturation

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