Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids

Lo, Wei Cheng; Sposito, Garrison; Majer, Ernest L.

doi:10.1007/s10665-008-9254-y

Cited by 21 publications

(11 citation statements)

References 43 publications

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“…The fast P wave has the largest change owing to the identical orientation of initial percolation and waveinduced forward motion of the fluid and solid (Lo et al 2009), while the propagations of slow P wave and S wave are scarcely influenced and no longer analyzed. Although the difference is small, the effect by the initial seepage is non-ignorable, especially in circumstances for micro mechanism explanation.…”

Section: Ratio Of Initial Flow Rate and Solid Scalar Potential And VImentioning

confidence: 99%

Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores

Han

Zheng

Chen

et al. 2018

J Petrol Explor Prod Technol

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An improved model based on Biot poroelastic theory is presented incorporating the initial seepage flow in the matrix. The proposed model quantifies wave propagation in the oil field development process as VSP, transient well tests, and seismic production technology. Porosity variation, fluid-solid compressibility, and pseudo-threshold pressure gradient in low permeability reservoir are simultaneously considered, resulting in a modified form of continuity and motion equations. Integrating the equations and decomposition for the fluid-solid displacements helps to derive the analytical wave vectors of the fast P, slow P, and S waves in porous media. The sensitivity of affecting factors, such as petrophysical parameter, fluid property, and vibration frequency, on the wave velocity and attenuation is subsequently evaluated. Furthermore, the Biot model can be considered a special situation when the initial flow rate in this model tends to zero. The increase in initial percolating rate, expressed by the ratio of initial flow rate and solid scalar potential, causes an obvious decrease in the fast P wave velocity and an increase in its quality factor. Propagation of the slow P wave and the S wave is scarcely influenced. Low vibration frequency and low permeability also contribute to a large difference between the wave propagation parameters of the improved and Biot models. Cognition of the proportion in the inertia and viscosity effects is helpful in analyzing the complicated multiple mechanisms in wave propagation in the actual developed layer.

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Section: Ratio Of Initial Flow Rate and Solid Scalar Potential And VImentioning

confidence: 99%

Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores

Han

Zheng

Chen

et al. 2018

J Petrol Explor Prod Technol

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“…They recovered behavior similar to that shown in Figure 12, with increasing velocities for frequencies exceeding 100 Hz. Lo et al (2005Lo et al ( , 2009, who plotted phase velocities for waves propagating in a medium containing two fluids, give results for four frequencies (50,100,150,and 200 Hz). The general trend is one of increasing velocities with increasing frequency, as indicated in Figure 12.…”

Section: Longitudinal Displacementsmentioning

confidence: 99%

“…For these modes (P2, P3, and P4), the attenuation starts to increase significantly at around 100 Hz. Neither Tuncay and Corapcioglu (1996) nor Lo et al (2005Lo et al ( , 2009) plot the attenuation coefficients as functions of frequency for their two-phase calculations. However, their plots of attenuation coefficients for various frequencies do display a similar trend: larger attenuation coefficients at higher frequencies.…”

Section: Longitudinal Displacementsmentioning

confidence: 99%

“…Such approaches are too numerous to provide a comprehensive review in this Introduction. Therefore, I point out some representative studies that treated single phase flow (Garg, 1971;Pride et al, 1992), and two-phase flow (Berryman et al, 1988;Santos, 1990;Tuncay, 1995;Tuncay andCorapcioglu, 1996, 1997;Lo et al, 2005Lo et al, , 2009) for a homogeneous medium. Recently, the two-phase work was extended to a medium containing smoothly varying heterogeneity in Vasco and Minkoff (2012).…”

Section: Introductionmentioning

confidence: 99%

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On the propagation of a disturbance in a smoothly varying heterogeneous porous medium saturated with three fluid phases

Vasco

2013

GEOPHYSICS

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From the equations governing the deformation of a porous medium containing three fluid phases, I derive expressions for the phase velocity of the various modes of displacement. These expressions are valid for a medium with smoothly varying heterogeneity. There is a single mode of transverse displacement, similar in nature to an elastic shear wave. The four-phase velocities of the longitudinal modes of displacement are derived from the solutions of a quartic equation. The coefficients of the polynomial equation are written as linear sums of the determinants of 4 × 4 matrices. The matrices contain various combinations of the parameters from the governing equations. The three-phase expressions are compared to two-phase estimates for the case in which one of the fluid saturations vanishes. Also, in a numerical illustration, velocity variations of around 10% are associated with the cyclic injection of carbon dioxide and water into an oil-saturated reservoir.

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“…It is based on the continuum mixture theory, and is general enough to account for the changes in capillary pressure and viscous/inertial coupling among constituents. Lo et al [32] applied the Fourier transform to decouple the poroelasticity equations derived in Ref. [31] into three Helmholtz equations.…”

Section: Introductionmentioning

confidence: 99%

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

Kumar

Saini

2012

Appl. Math. Mech.-Engl. Ed.

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The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.

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Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids

Cited by 21 publications

References 43 publications

Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores

Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores

On the propagation of a disturbance in a smoothly varying heterogeneous porous medium saturated with three fluid phases

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

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