Simulation of Stoneley wave reflection from porous formation in borehole using FDTD method

Ou, Weiming; Wang, Zhuwen

doi:10.1093/gji/ggz144

Cited by 14 publications

(10 citation statements)

References 37 publications

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“…A 2D calculation of a cave can also show the main characteristics of the problem studied [15]. The staggered-grid finite difference method is used to simulate the propagation of elastic waves in our simulation [6]. The wave equation of velocity stress in isotropic media in cylindrical coordinates is as follows:…”

Section: Fd Methods For Elastic Wave Equationmentioning

confidence: 99%

“…In the equations mentioned above, the subscripts i and j in brackets refer to spatial index of nodes in x and z directions, respectively, the superscript n represents the time discrete index, τ rr , τ θθ and τ zz refer to normal stress in x, θ and z directions, τ rz is shear stress, ∆t is the time step, L 1 R and L 1 Z are second-order difference operators of space, and the parameters ρ and µ represent the density and shear moduli of the medium. On the medium interface, the arithmetic mean value of ρ and the harmonic mean value of µ are employed; on the solid-liquid interface, µ is set to 0 [6,7]. σ i f (i,j) and σ j f (i,j) are arithmetic average operators and defined as:…”

Section: Fd Methods For Elastic Wave Equationmentioning

confidence: 99%

“…∆r ≤ v min /10 f max (10) where v min is the minimum velocity of numeric model, and f max is the maximum frequency of the source [6,7]. The stability condition of the second-order FD is…”

Section: Fd Methods For Elastic Wave Equationmentioning

confidence: 99%

“…Therefore, it is very important to grasp the effect of caves on borehole acoustic wave propagation, which plays an important role in the detection and evaluation of caves. Currently, the effect of fractured and gas-bearing reservoirs on borehole acoustics has been investigated [6][7][8]. However, there are few studies on the acoustic-logging response of caves.…”

Section: Introductionmentioning

confidence: 99%

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Numeric Simulation of Acoustic-Logging of Cave Formations

Wang

2020

Energies

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The finite difference (FD) method of monopole source is used to simulate the response of full-wave acoustic-logging in cave formations. The effect of the cave in the formation of borehole full-waves was studied. The results show that the radius of cave is not only linearly related to the first arrival of the compressional wave (P-wave), but also to the energy of the shear wave (S-wave). The converted S (S–S wave) and P-waves (S–P wave) are formed when the S-wave encounters the cave. If the source distance is small, the S–S and S–P waves are not separated, and the attenuation of the S-wave is not large, due to superposition of the converted waves. The S–P wave has been separated from the S-wave when the source distance is large, so the attenuation of the S-wave increases. The amplitude of the P and S–waves changes most when the distance of the cave to the borehole wall reaches a certain value; this value is related to the excitation frequency. The amplitude of the Stoneley wave (ST wave) varies directly with the radius of cave. If the radius of the cave is large, the energy of ST wave is weak. The scattered wave is determined by the radius and position of the cave. The investigation depth of a monopole source is limited. When the distance of the cave to the borehole wall exceeds the maximum investigation depth, the borehole acoustic wave is little affected by the cave. In actual logging, the development of the cave can be evaluated by using the first arrival of the P-wave and the energy of the S and ST waves.

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Section: Fd Methods For Elastic Wave Equationmentioning

confidence: 99%

Section: Fd Methods For Elastic Wave Equationmentioning

confidence: 99%

Section: Fd Methods For Elastic Wave Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numeric Simulation of Acoustic-Logging of Cave Formations

Wang

2020

Energies

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“…Yan [40] et.al numerically simulate the acoustic fields excited by a point source in the borehole surrounded by a porous formation using the 3D staggered grid stress-velocity finite difference method. Ou [41] used the FDTD algorithm to simulate the wave propagation in a borehole within a porous medium and studied the characteristics of the Stoneley wave reflection. These studies show that much research has been performed on the acoustic logs with a two-phase porous medium.…”

Section: Introductionmentioning

confidence: 99%

Acoustic Wave Propagation in a Borehole with a Gas Hydrate-Bearing Sediment

Liu

Zhang

et al. 2022

JMSE

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A knowledge of wave propagation in boreholes with gas hydrate-bearing sediments, a typical three-phase porous medium, is of great significance for better applications of acoustic logging information on the exploitation of gas hydrate. To study the wave propagation in such waveguides based on the Carcione–Leclaire three-phase theory, according to the equations of motion and constitutive relations, a staggered-grid finite-difference time-domain (FDTD) scheme and a real axis integration (RAI) algorithm in a two-dimensional (2D) cylindrical coordinate system are proposed. In the FDTD scheme, the partition method is used to solve the stiff problem, and the nonsplitting perfect matched layer (NPML) scheme is extended to solve the problem of the false reflection waves from the artificial boundaries of the computational region. In the RAI algorithm, combined with six boundary conditions, the displacement potentials of waves are studied to calculate the borehole acoustic wavefields. The effectiveness is verified by comparing the results of the two algorithms. On this basis, the acoustic logs within a gas hydrate-bearing sediment are investigated. In particular, the wave field in a borehole is analyzed and the amplitude of a Stoneley wave under different hydrate saturations is studied. The results indicate that the attenuation coefficient of the Stoneley wave increases with the increase of gas hydrate saturation. The acoustic responses in a borehole embedded in a horizontally stratified hydrate formation are also simulated by using the proposed FDTD scheme. The result shows that the amplitude of the Stoneley wave from the upper interface is smaller than that from the bottom interface.

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Extinction of Stoneley waves in stratified media with diffused interfaces

Kuznetsov

2021

Int J Mech Mater Des

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Simulation of Stoneley wave reflection from porous formation in borehole using FDTD method

Cited by 14 publications

References 37 publications

Numeric Simulation of Acoustic-Logging of Cave Formations

Numeric Simulation of Acoustic-Logging of Cave Formations

Acoustic Wave Propagation in a Borehole with a Gas Hydrate-Bearing Sediment

Extinction of Stoneley waves in stratified media with diffused interfaces

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