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Alexandrov Dmitriy , Saint-Petersburg State University

Numerical modeling: Tube-wave reflections in cased borehole. Alexandrov Dmitriy , Saint-Petersburg State University. Outline. 1D effective wavenumber approach. Modeling approaches. Outline. Model 1. Model 2. Conclusions. Model 3. Limitations.

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Alexandrov Dmitriy , Saint-Petersburg State University

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  1. Numerical modeling:Tube-wave reflections in cased borehole Alexandrov Dmitriy, Saint-Petersburg State University

  2. Outline 1D effective wavenumber approach Modeling approaches Outline Model 1 Model 2 Conclusions Model 3 Limitations • Modeling approaches: • 1D effective wavenumber approach • finite-difference • Wave field in cased borehole • wave field in isotropic homogeneous fluid • wave field in isotropic homogeneous elastic media • Reflection from geological interfaces behind casing; • Reflection from corroded section of the casing; • Response of perforation in cased borehole: • Idealized disk-shaped perforation • Idealized zero-length disk-shaped perforation • 1D approach limitations; • Conclusions. Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  3. Outline 1D effective wavenumber approach Modeling approaches Introduction Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  4. Modeling approaches Outline 1D effective wavenumber approach Modeling approaches Model 1 Model 2 Conclusions Model 3 Limitations • Finite-difference (FD) code • flexible • little analytical insight • 1D effective wavenumber approach • Attractive for analysis • Approximate • Validity for cased borehole is unknown • Validate 1D approach using FD code Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  5. Solution form: Outline Modeling approaches 1D effective wavenumber approach 1D effective wavenumber approach Conclusions Results Limitations Wavefield in cased borehole Helmholtz equations: Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  6. Boundary conditions: • continuity of pressure: • continuity of fluid flow: Outline Modeling approaches 1D effective wavenumber approach 1D effective wavenumber approach Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  7. Outline Modeling approaches 1D effective wavenumber approach 1D effective wavenumber approach Conclusions Results Limitations Wavefield in cased borehole • Multilayeredmodel Boundary conditions: • continuity of pressure: • continuity of fluid flow: Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  8. Outline 1D effective wavenumber approach Modeling approaches Wave field in isotropic homogeneous fluid Conclusions Results Limitations Wavefield in cased borehole Motion equation: Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  9. Outline 1D effective wavenumber approach Modeling approaches Wave field in isotropic homogeneous fluid Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  10. Outline 1D effective wavenumber approach Modeling approaches Wave field in isotropic homogeneous elastic media Conclusions Results Limitations Wavefield in cased borehole Motion equation: Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  11. Outline 1D effective wavenumber approach Modeling approaches Boundary conditions Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  12. Outline 1D effective wavenumber approach Modeling approaches Reflection from geological interfaces behind casing Conclusions Results Limitations Wavefield in cased borehole Reflection coefficient for tube wave Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  13. Outline 1D effective wavenumber approach Modeling approaches Reflection from corroded section of the casing Conclusions Results Limitations Wavefield in cased borehole Reflection of tube wave from three different types of corroded section. Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  14. Outline 1D effective wavenumber approach Modeling approaches Idealized perforation in cased borehole Conclusions Results Limitations Wavefield in cased borehole Considered models: • Finite-length perforation (10 cm) • Zero-length perforation (break in casing) Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  15. Outline 1D effective wavenumber approach Modeling approaches Idealized perforation in cased borehole Conclusions Results Limitations Wavefield in cased borehole Reflection of the tube wave from perforation with 10 cm length . Reflection of the tube wave from zero-length perforation. Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  16. Outline 1D effective wavenumber approach Modeling approaches Limitations Conclusions Results Limitations Wavefield in cased borehole Low frequency approximation for tube-wave slowness (White J.E. 1984): Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  17. Outline 1D effective wavenumber approach Modeling approaches Limitations Conclusions Results Limitations Wavefield in cased borehole Relative error defined as: Considered model: Relative error of 1D approach Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  18. Reflection coefficients Finite-difference code 1D approach Outline 1D effective wavenumber approach Modeling approaches Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  19. Reflection coefficients Finite-difference code 1D approach Outline 1D effective wavenumber approach Modeling approaches Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  20. Reflection coefficients Finite-difference code 1D approach Outline 1D effective wavenumber approach Modeling approaches Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  21. Outline 1D effective wavenumber approach Modeling approaches Conclusions Conclusions Results Limitations Wavefield in cased borehole • Validated 1D approach for • multi-layered media (cased boreholes) • inhomogeneous borehole casing • idealized perforations in cased borehole • Defined the limitations for 1D approach Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  22. Outline 1D effective wavenumber approach Modeling approaches Thank you for attention! Conclusions Results Limitations Wavefield in cased borehole Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  23. Outline 1D effective wavenumber approach Modeling approaches References Model 1 Model 2 Conclusions Model 3 Limitations • References • Bakulin, A., Gurevich, B., Ciz, R., and Ziatdinov S., 2005, Tube-wave reflection from a porous permeable layer with an idealized perforation: 75th Annual Meeting, Society of Exploration Geophysicists, Expanded Abstract, 332-335. • Krauklis, P. V., and A. P. Krauklis, 2005, Tube Wave Reflection and Transmission on the Fracture: 67th Meeting, EAGE, Expanded Abstracts, P217. • Medlin, W.L., Schmitt, D.P., 1994, Fracture diagnostics with tube-wave reflections logs: Journal of Petroleum Technology, March, 239-248. • Paige, R.W., L.R. Murray, and J.D.M. Roberts, 1995, Field applications of hydraulic impedance testing for fracture measurements: SPE Production and Facilities, February, 7-12. • Tang, X. M., and C. H. Cheng, 1993, Borehole Stoneley waves propagation across permeable structures: Geophysical Prospecting, 41, 165-187. • Tezuka, K., C.H. Cheng, and X.M. Tang, 1997, Modeling of low-frequency Stoneley-wave propagation in an irregular borehole: Geophysics, 62, 1047-1058. • White, J. E., 1983, Underground sound, Elsevier. • Winkler, K. W., H. Liu, and D.L. Johnson, 1989, Permeability and borehole Stoneley waves: Comparison between experiment and theory: Geophysics, 54, 66–75. Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

  24. Outline 1D effective wavenumber approach Modeling approaches Formation parameters Model 1 Model 2 Conclusions Model 3 Limitations Tube-wave reflections in cased borehole AlexandrovDmitriy, StPSU, Saint-Petersburg, Russia.

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