Abstract
The conventional acoustic logging interpretation method, which is based on vertical wells that penetrate isotropic formations, is not suitable for horizontal and deviated wells penetrating anisotropic formations. This unsuitability is because during horizontal and deviated well drilling, cuttings will splash on the well wall or fall into the borehole bottom and form a thin bed of cuttings. In addition, the high velocity layers at different depths and intrinsic anisotropy may affect acoustic logging measurements. In this study, we examine how these factors affect the acoustic wave slowness measured in horizontal and deviated wells that are surrounded by an anisotropic medium using numerical simulation. We use the staggered-grid finite difference method in time domain (FDTD) combined with hybrid-PML. First, we acquire the acoustic slowness using a simulated array logging system, and then, we analyze how various factors affect acoustic slowness measurements and the differences between the effects of these factors. The factors considered are high-velocity layers, thin beds of cuttings, dipping angle, formation thickness, and anisotropy. The simulation results show that these factors affect acoustic wave slowness measurements differently. We observe that when the wavelength is much smaller than the distance between the borehole wall and high velocity layer, the true slowness of the formation could be acquired. When the wavelengths are of the same order (i.e., in the near-field scenarios), the geometrical acoustics theory is no longer applicable. Furthermore, when a thin bed of cuttings exists at the bottom of the borehole, Fermat's principle is still applicable, and true slowness can be acquired. In anisotropic formations, the measured slowness changes with increments in the dipping angle. Finally, for a measurement system with specific spacing, the slowness of a thin target layer can be acquired when the distance covered by the logging tool is sufficiently long. Based on systematical simulations with different dipping angles and anisotropy in homogenous TI media, slowness estimation charts are established to quantitatively determine the slowness at any dipping angle and for any value of the anisotropic ratio. Synthetic examples with different acoustic logging tools and different elastic parameters demonstrate that the acoustic slowness estimation method can be conveniently applied to horizontal and deviated wells in TI formations with high accuracy.
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References
Bayliss, A., Jordan, K. E., LeMesurier, B. J., et al., 1986, A fourth-order accurate finite-difference scheme for the computation of elastic waves: Bulletin of the Seismological Society of America, 76(4), 1115–1132.
Bigelow, E. L., and Cleneay, C. A., 1992, A new frontier: log interpretation in horizontal wells: 33rd Annual Logging Symposium, SPWLA, 14–17 June, Texas, USA.
Cheng, N. Y., 1994, Borehole wave propagation in isotropic and anisotropic media: three dimensional finite difference approach: PhD thesis, Massachusetts Institute of Technology.
Cheng, N. Y., Cheng, C. H., and Toksöz, M. N., 1995, Borehole wave propagation in three dimensions: The Journal of the Acoustical Society of America, 97, 3483–3493.
Chen, M. Y., He, X. P., and Jin, X. H., 2013, Study on acoustic slowness response features in horizontal wells: World Well Logging Technology (in Chinese), 4, 38–41.
Clavier, C., 1991, The challenge of logging horizontal wells: The Log Analyst, 32(2), 63–84.
Cong, J. S., and Qiao, W. X., 2008, Simulated response of acoustic log in horizontal borehole placing on interface of two formations: Well Logging Technology (in Chinese), 32(1), 29–32.
Dablain, M. A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51(1), 54–66.
Gianzero, S. C., Chemali, R. E., and Su, S. M., 1992, Induction, resistivity, and MWD tools in horizontal wells: SPE International Meeting on Petroleum Engineering, 24-27 March, Beijing, China, SPE 22347, 191–199.
Hu, Z. P., Guan, L. P., Gu, L. X., et al., 2004, Wide angle seismic wave field analysis and imaging method below the high velocity shield layers: Chinese Journal of Geophysics (in Chinese), 47(1), 88–94.
Komatitsch, D., and Martin, R., 2007, An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation: Geophysics, 72(5), 155–167.
Leslie, H. D., and Randall, C. J., 1992, Multipole sources in boreholes penetrating anisotropic formations: Numerical and experimental results: The Journal of the Acoustical Society of America, 91, 12–27.
Levander, A. R., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53(11), 1425–1436.
Liang, K., 2009, The study on propagation feature and forward modeling of seismic wave in TI media: PhD thesis, China University of Petroleum, Dongying, 17–21.
Lin, W. J., Wang, X. M., and Zhang, H. L., 2006, Acoustic wave propagation in a borehole penetrating an inclined layered formation: Chinese Journal of Geophysics (in Chinese), 49(1), 284–294.
Liu, J., Ma, J., and Yang, H., 2009, The study of perfectly matched layer absorbing boundaries for SH wave fields: Applied Geophysics, 6(3), 267.
Madariaga, R., 1976, Dynamics of an expanding circular fault: Bulletin of the Seismological Society of America, 66(3), 639–666.
Mallan, R. K., Ma, J., and Torres-Verdín, C., 2009, 3D Numerical simulation of borehole sonic measurements acquired in dipping, anisotropic, and invaded formations: 50th Annual Logging Symposium, SPWLA, 21–24 June, Texas, USA.
Meza-Fajardo, K. C., and Papageorgiou, A. S., 2008, A nonconvolutional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: stability analysis: Bulletin of the Seismological Society of America, 98(4), 1811–1836.
Passey, Q. R., Yin, H., Rendeiro, C. M., and Fitz, D. E., 2005, Overview of high-angle and horizontal well formation evaluation: issues, learning, and future directions: 46th Annual Logging Symposium, SPWLA, 26–29 June, New Orleans, USA.
Singer, J. M., 1992, An example of log interpretation in horizontal wells: The Log Analyst, 33(2), 85–95.
Song, R., Ma, J., and Wang, K., 2005, The application of the nonsplitting perfectly matched layer in numerical modeling of wave propagation in poroelastic media: Applied Geophysics, 2(4), 216–222.
Tang, X. M., and Cheng, A., 2004, Quantitative borehole acoustic methods: Petroleum Industry Press Beijing, 24, 20–43.
Tao, G., Gao, K., Wang, B., and Ma, Y., 2007, Application of multipole array sonic logging to acid hydralic fracturing: Applied Geophysics, 4(2), 133–137.
Tao, G., He, F. J., Yue, W. Z., and Chen, P., 2008, Processing of array sonic logging data with multi-scale STC technique: Petroleum Science, 5, 238.
Tao, G., Zhang, Y. S., and Zhang, H. E., 2001, 3D finite difference simulating program for acoustic logging: Well Logging Technology (in Chinese), 25(4), 273–277.
Virieux, J., 1984, SH wave propagation in heterogeneous media: Velocity-stress finite-difference method: Geophysics, 49(11), 1933–1957.
Virieux, J., 1986, P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method: Geophysics, 51(4), 889–901.
Wang, H. G., Liu, X. S., and Ding, G., et al., 1995, An experimental study of transport of drilling cutting in a horizontal well: Acta Petrolei Sinica (in Chinese), 16(4), 125–132.
Wang, H., Tao, G., and Shang, X. F., 2013, Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes: Applied Geophysics, 10(4), 384–396.
Wang, R. J., Torres-Verdín, C., Huang, S., and Herrera, W., 2015, Interpretation of sonic waveforms acquired in high-angle and horizontal wells: 56th Annual Logging Symposium, SPWLA, 18-22 July, Oklahoma, USA.
Wei, Z. T., and Chen, X. L., 2014, Analysis of borehole acoustic field and establishment of acoustic slowness correction chart in deviated formations: Acta Acustica (in Chinese), 40(3), 437–445.
Winterstein, D. F., 1990, Velocity anisotropy terminology for geophysicists: Geophysics, 55(8), 1070–1088.
Wu, G. C., 2006, Propagation and imaging of seismic waves in anisotropic media: China University of Petroleum Press, Shandong, 26–32.
Zhang, K., Tao, G., Li, J. X., et al., 2014, 3D FDM modeling of acoustic reflection logging in a deviated well: 76th EAGE Annual Meeting, Expanded Abstracts, Th P10 03.
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The authors would like to thank the editor and anonymous reviewers for their valuable comments and suggestions that significantly improved the manuscript.
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This study was supported by National Natural Science Foundation of China (No. 41204094) and Science Foundation of China University of Petroleum, Beijing (No. 2462015YQ0506).
Liu He received his bachelor’s degree from China University of Petroleum (Beijing) in 2012 and now is a PhD student in China University of Petroleum (Beijing). He works on array acoustic logging numerical simulation and acoustic logging data processing.
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Liu, H., Wang, B., Tao, G. et al. Study on the simulation of acoustic logging measurements in horizontal and deviated wells. Appl. Geophys. 14, 337–350 (2017). https://doi.org/10.1007/s11770-017-0637-6
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DOI: https://doi.org/10.1007/s11770-017-0637-6