Alexandrov Dmitriy, Saint-Petersburg State University

1
Numerical modelingTube-wave reflections in
cased borehole

• Alexandrov Dmitriy,
  Saint-Petersburg State University

2
Outline
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Model 1
Model 2
Model 3
Conclusions

• 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 Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
3
Introduction
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
4
Modeling approaches
Modeling approaches
Outline
1D effective wavenumber approach
Limitations
Model 1
Model 2
Model 3
Conclusions

• 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 Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
5
1D effective wavenumber approach
Outline
Modeling approaches
1D effective wavenumber approach
Limitations
Results
Conclusions
Wavefield in cased borehole
Helmholtz equations

Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
6
1D effective wavenumber approach
Outline
Modeling approaches
1D effective wavenumber approach
Limitations
Results
Conclusions
Wavefield in cased borehole
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
7
1D effective wavenumber approach
Outline
Modeling approaches
1D effective wavenumber approach
Limitations
Results
Conclusions
Wavefield in cased borehole

• Multilayered model
• Boundary conditions
• continuity of pressure
• continuity of fluid flow

Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
8
Wave field in isotropic homogeneous fluid
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Motion equation
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
9
Wave field in isotropic homogeneous fluid
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
10
Wave field in isotropic homogeneous elastic media
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Motion equation
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
11
Boundary conditions
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole

Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
12
Reflection from geological interfaces behind
casing
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Reflection coefficient for tube wave
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
13
Reflection from corroded section of the casing
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Reflection of tube wave from three different
types of corroded section.
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
14
Idealized perforation in cased borehole
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Considered models

• Finite-length perforation (10 cm)
• Zero-length perforation
• (break in casing)

Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
15
Idealized perforation in cased borehole
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
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 Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
16
Limitations
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole

• Low frequency approximation
• for tube-wave slowness
• (White J.E. 1984)

Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
17
Limitations
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Relative error defined as
Considered model
Relative error of 1D approach
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
18
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
19
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
20
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
21
Conclusions
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
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 Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
22
Thank you for attention!
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Results
Conclusions
Wavefield in cased borehole
Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
23
References
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Model 1
Model 2
Model 3
Conclusions

• 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, 6675.

Tube-wave reflections in cased borehole Alexandrov
Dmitriy, StPSU, Saint-Petersburg, Russia.
24
Formation parameters
Outline
1D effective wavenumber approach
Modeling approaches
Limitations
Model 1
Model 2
Model 3
Conclusions
Longitudinal velocity (m/s) Shear velocity (m/s) Density (kg/m3)
Elastic half-spaces 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, StPSU, Saint-Petersburg, Russia.