1887
Volume 61, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three‐dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre‐corrected fast Fourier transform (pFFT)‐accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre‐conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.2012.01070.x
2012-07-02
2024-04-29
Loading full text...

Full text loading...

References

  1. AbubakarA., Van den BergM.P. and HabashyT.M.2006. An integral equation approach for 2.5‐dimensional forward and inverse electromagnetic scattering. Geophysical Journal International 165, 744–762.
    [Google Scholar]
  2. AvdeevD.B., KuvshinovA.V. and EpovaK.A.2002b. Three‐dimensional modeling of electromagnetic logs from inclined‐horizontal wells. Physics of the Solid Earth 38, 975–980.
    [Google Scholar]
  3. AvdeevD.B., KuvshinovA.V., PankratovO.V. and NewmanG.A.2002a. Three‐dimensional induction logging problems, part I: An integral equation solution and model comparisons. Geophysics 67, 413–426.
    [Google Scholar]
  4. ChewW.C., NieZ.P., LiuQ.H. and AndersonB.1991. An efficient solution for response of electrical well logging tools in a complex environment. IEEE Transactions on Geoscience and Remote Sensing 29, 308–313.
    [Google Scholar]
  5. DavydychevaS., HomanD. and MinerboG.2009.Triaxial induction tool with electrode sleeve: FD modeling in 3D geometries. Journal of Applied Geophysics 67, 98–108.
    [Google Scholar]
  6. DruskinV.L., LeeP. and KnizhnermanL.A.2000. Method, apparatus and article of manufacture for solving 3D Maxwell Equations in inductive logging applications. United States Patent, Patent number: 6,115,670.
  7. FangS., GaoG.Z. and Torres‐VerdinC.2004. Fast 3D Modeling of Borehole Induction Measurements in Dipping and Anisotropic Formations using a Novel Approximation Technique. Petrophysics 45(4).
    [Google Scholar]
  8. FangS., GaoG.Z. and Torres‐VerdinC.2006. Efficient 3D electromagnetic modeling in the presence of anisotropic conductive media, using integral equations. Exploration Geophysics 37, 239–244.
    [Google Scholar]
  9. FarquharsonC.G., DuckworthK. and OldenburgD.W.2006. Comparison of integral equation and physical scale modeling of the electromagnetic responses of models with large conductivity contrasts. Geophysics 71, 169–177.
    [Google Scholar]
  10. HanW.S.2004. 3D finite element simulation method of induction and MWD tools . PhD dissertation, University of Houston .
  11. KaufmanA.A. and DashevskyY.A.2003. Principle of Induction Logging. Methods in Geochemistry and Geophysics 38, 627–637
    [Google Scholar]
  12. LiuC. and ShenL.C.1991. Response of electromagnetic‐pulse logging sonde in axially symmetrical formation. IEEE Transactions on Geoscience and Remote Sensing 29, 214–221.
    [Google Scholar]
  13. McLarenA.D.1963. Optimal numerical integration on a sphere. Mathematics of Computation 17, 361–383.
    [Google Scholar]
  14. NamM.J., PardoD. and Torres‐VerdinC.2010. Simulation of triaxial induction measurements in dipping, invaded, and anisotropic formations using a Fourier series expansion in a nonorthogonal system of coordinates and self‐adaptive hp finite‐element method. Geophysics 75, F83–F95.
    [Google Scholar]
  15. NieX.C., LiL.W., YuanN., YeoT.S. and GanY.B.2005. Precorrected‐FFT solution of the volume integral equation for 3‐D inhomogeneous dielectric objects. IEEE Transactions on Antennae and Propagation 53, 313–320.
    [Google Scholar]
  16. SaadY.1994. ILUT: A dual threshold incomplete LU factorization. Numerical Linear Algebra with Applications 1, 387–402.
    [Google Scholar]
  17. SchaubertD.H., WiltonD.R. and GlissonA.W.1984. A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies. IEEE Transactions on Antennae and Propagation 32, 77–85.
    [Google Scholar]
  18. StreichR.2009. 3D finite‐difference frequency‐domain modeling of controlled‐source electromagnetic data: Direct solution and optimization for high accuracy. Geophysics 74, P. F95–F105.
    [Google Scholar]
  19. TeixeiraF.L., MartinL.S. and BittarM.S.2005. Modeling of EM logging tools in arbitrary 3‐D borehole geometries using PML‐FDTD. IEEE Transactions on Geoscience and Remote Sensing Letters 2, 78–81.
    [Google Scholar]
  20. Torres‐Verdín, C. and HabashyT.M.1994. Rapid 2.5‐dimensional forward modeling and inversion via a new nonlinear scattering approximation. Radio Science Vol. 29, No. 4 , 1051–1079.
    [Google Scholar]
  21. YuanN., NieX.C. and LiuR.2010. Electromagnetic Field Response of Triaxial Induction Logging Tools in 1‐D Multi‐Layered Anisotropic Formations. 2010 AP‐S International Symposium and URSI National Radio Science Meeting, Toronto , Canada , July 11–17, 2010.
  22. ZhangZ.Q. and LiuQ.H.2003. Application of the BCGS‐FFT method to 3‐D induction well logging problems. IEEE Transactions on Geoscience and Remote Sensing 41, 998–1004.
    [Google Scholar]
  23. ZhdanovM.S., LeeS.K. and YoshiokaK.2006. Integral equation method for 3D modeling of electromagnetic fields in complex structures with inhomogeneous background conductivity. Geophysics 67, G333–G345.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.2012.01070.x
Loading
/content/journals/10.1111/j.1365-2478.2012.01070.x
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): 3D; Fast algorithm; High conductivity contrast; Induction logging; Integral equation

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error