Numerical modeling Tubewave reflections in cased borehole Alexandrov

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

Outline Modeling approaches Model 2 Model 3 Model 1 1 D effective wavenumber approach Conclusions Limitations Outline o Modeling approaches: n n o Wave field in cased borehole n n o o o n o 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: n o 1 D effective wavenumber approach finite-difference Idealized disk-shaped perforation Idealized zero-length disk-shaped perforation 1 D approach limitations; Conclusions. Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

Outline Modeling approaches Results Wavefield in cased borehole 1 D effective wavenumber approach Conclusions Limitations Introduction Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

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

Outline Modeling approaches Results Wavefield in cased borehole 1 D effective wavenumber approach Conclusions Limitations 1 D effective wavenumber approach o Helmholtz equations: Solution form: Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

Outline Modeling approaches Results Wavefield in cased borehole 1 D effective wavenumber approach Conclusions Limitations 1 D effective wavenumber approach Boundary conditions: o continuity of pressure: o continuity of fluid flow: Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

Outline Modeling approaches Results Wavefield in cased borehole 1 D effective wavenumber approach Conclusions Limitations 1 D effective wavenumber approach o Multilayered model Boundary conditions: n continuity of pressure: n continuity of fluid flow: Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

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

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

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

Outline Modeling approaches Results Wavefield in cased borehole 1 D effective wavenumber approach Conclusions Limitations Boundary conditions o o Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

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

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

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

Outline Modeling approaches Results Wavefield in cased borehole 1 D effective wavenumber approach Conclusions Limitations Idealized perforation 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 Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

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

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

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

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

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

Outline Modeling approaches Results Wavefield in cased borehole 1 D effective wavenumber approach Conclusions Limitations Conclusions o Validated 1 D approach for n n n o multi-layered media (cased boreholes) inhomogeneous borehole casing idealized perforations in cased borehole Defined the limitations for 1 D approach Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

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

Outline Model 1 Modeling approaches Model 2 Model 3 1 D effective wavenumber approach Conclusions Limitations References o o o o o References Bakulin, A. , Gurevich, B. , Ciz, R. , and Ziatdinov S. , 2005, Tube-wave reflection from a porous permeable layer with an idealized perforation: 75 th 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: 67 th Meeting, EAGE, Expanded Abstracts, P 217. 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 Stoneleywave 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 Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.

Outline Model 1 Modeling approaches Model 2 Model 3 1 D effective wavenumber approach Conclusions Limitations Formation parameters Longitudinal velocity (m/s) Shear velocity (m/s) Density (kg/m 3) Elastic halfspaces 3500 2500 3400 Fluid 1500 - 1000 Casing 1 (steel) 6000 3000 7000 Casing 2 (plastic) 2840 1480 1200 Layer 1 3100 1800 2600 Layer 2 3700 2400 3000 Corroded section 1 1200 600 1400 Corroded section 2 3000 1500 3500 Corroded section 3 4200 2100 4900 Tube-wave reflections in cased borehole Alexandrov. Dmitriy, St. PSU, Saint-Petersburg, Russia.