Elastic wave propagation in a fluid‐filled borehole and synthetic acoustic logs

Cheng, C. H.; Toksöz, M. Nafi

doi:10.1190/1.1441242

Cited by 286 publications

(130 citation statements)

References 5 publications

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“…We use the modeling technique described by Tsang and Rader [1979], Cheng and Toksöz [1981] and Kurkjian and Chang [1986]. Assuming that the borehole is an infinite fluid-filled cylinder in an infinite elastic medium, the excitation of a receiver located at a distance z from the transmitter is the sum of a direct pulse through the borehole fluid p i and of a formation response pulse p r given by…”

Section: Waveform Modelingmentioning

confidence: 99%

Sonic waveform attenuation in gas hydrate‐bearing sediments from the Mallik 2L‐38 research well, Mackenzie Delta, Canada

2002

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[1] The Mallik 2L-38 research well was drilled to 1150 m under the Mackenzie Delta, Canada, and penetrated a subpermafrost interval where methane hydrate occupies up to 80% of the pore space. A suite of high-quality downhole logs was acquired to measure in situ the physical properties of these hydrate-bearing sediments. Similar to other hydrate deposits, resistivity and compressional and shear sonic velocity data increase with higher hydrate saturation owing to electrical insulation of the pore space and stiffening of the sediment framework. In addition, sonic waveforms show strong amplitude losses of both compressional and shear waves in intervals where methane hydrate is observed. We use monopole and dipole waveforms to estimate compressional and shear attenuation. Comparing with hydrate saturation values derived from the resistivity log, we observe a linear increase in both attenuation measurements with increasing hydrate saturation, which is not intuitive for stiffening sediments. Numerical modeling of the waveforms allows us to reproduce the recorded waveforms and illustrate these results. We also use a model for wave propagation in frozen porous media to explain qualitatively the loss of sonic waveform amplitude in hydratebearing sediments. We suggest that this model can be improved and extended, allowing hydrate saturation to be quantified from attenuation measurements in similar environments and providing new insight into how hydrate and its sediment host interact.

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Section: Waveform Modelingmentioning

confidence: 99%

Sonic waveform attenuation in gas hydrate‐bearing sediments from the Mallik 2L‐38 research well, Mackenzie Delta, Canada

2002

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“…Although the source used in Figure 6 has an upper-half-power frequency at 20 kHz, there is significant energy at about 23 kHz. This is due to the excitation of the second mode of the pseudo-Rayleigh wave (Cheng and Toksoz, 1981;Paillet, 1980). The grid size used to calculate the waveform in Figure 6b gives a number of grid points per wavelength that is less than 10.…”

Section: -10mentioning

confidence: 99%

“…The first task is to compare finite difference acoustic logs with logs generated by the discrete wave number approach (Cheng and Toksoz, 1981). This will provide a useful cheek on the accuracy of the two methods since they are fundamentally different ways of solving the same problem and the nature of the numerical approximations in each case is entirely different.…”

Section: Introductionmentioning

confidence: 99%

Finite-difference synthetic acoustic logs

1986

International Journal of Rock Mechanics and Mining Sciences &am

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Synthetic seismograms of elastic wave propagation in a fluid-filled borehole were generated using both the finite difference technique and the discrete wavenumber summation technique. The latter is known to be accurate for both body and surface (gUided) waves. The finite difference grid has absorbing boundaries on two sides and axes of symmetry on the remaining two sides. A grid size no less than 10 points per wavelength was used. The far absorbing boundary was located at a distance of five to 10 radii from the borehole. Two types of solid-liquid interfaces were investigated: 1) a velocity gradient using the heterogeneous formulation, and 2) a sharp boundary using a second order Taylor expansion of the displacements. The results from the finite difference modeling were compared with the synthetic seismograms generated by the discrete wavenumber summation method. No comparison the heterogeneous formulation and the discrete wavenumber method has been made. The second order approximation to the solid-liquid interface produced seismograms that compared 'well with the discrete wavenumber seismograms. A detailed comparison between the seismograms generated by the two methods showed that the body waves (refracted P and S waves) are identical. while the gUided waves showed a slight difference in both phase and amplitude. These differences are believed to be due to the approximations introduced in the fluid-solid interface, the absorbing boundary at the edge of the grid, and the grid and time step sizes involved. Owing. to the fact that they are interface waves, the gulded waves, especially the higher modes, are much more sensitive to the above mentioned approximations.

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“…Among these, the discrete wave number method (DWM) (Cheng and Toksoz, 1981;Schmitt and Bouchon, 1985;Kurkjian and Chang, 1986;Wang and Tao, 2011), the fi nite difference in time domain (FDTD) (Cheng, 1994;Wang and Tang, 2003a;Wang and Tang, 2003b;Tao et al, 2008;Wang et al, 2009), and the finite element method (FEM) (Matuszyk and TorresVerdin, 2011;Wang et al, 2013) are commonly used to simulate the acoustic logging wave fi eld. The DWM is numerically fast, but is difficult to implement for nonaxial symmetric models, such as tool isolation design (Chen et al, 1998;Wang et al, 2009) and acoustic LWD tool eccentricity (Huang, 2003).…”

Section: Introductionmentioning

confidence: 99%

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

et al. 2013

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Abstract:In acoustic logging-while-drilling (ALWD) fi nite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fl uid-fi lled borehole and divides the borehole fl uid into two thin fl uid columns (radius ~27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fl uid in the borehole (the difference is >30 times), the stability and effi ciency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including fi eld-splitting PML (SPML), multiaxial PML(M-PML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the effi ciency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profi le was obtained using one d 0 . The optimal parameter space for the maximum value of the linear frequency-shifted factor (α 0 ) and the scaling factor (β 0 ) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

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Elastic wave propagation in a fluid‐filled borehole and synthetic acoustic logs

Cited by 286 publications

References 5 publications

Sonic waveform attenuation in gas hydrate‐bearing sediments from the Mallik 2L‐38 research well, Mackenzie Delta, Canada

Sonic waveform attenuation in gas hydrate‐bearing sediments from the Mallik 2L‐38 research well, Mackenzie Delta, Canada

Finite-difference synthetic acoustic logs

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

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