volume | PIER Journals

Abstract

The analytical formulae based on the generalized reflection and transmission coefficient matrices for cylindrically stratified media are used to simulate the borehole effect on multicomponent induction logging responses in various ratios of mud conductivity and formation conductivity and to investigate the tool's eccentricity effect on the responses of coplanar coils and coaxial coils. The simulated data show that the borehole effect and the tool's eccentricity effect on the response of coplanar coils is greater than that on the response of coaxial coils in most cases. Then we give an algorithm for the correction of borehole effect on multicomponent induction logging responses, and the algorithm is based on the above-mentioned formulae to build forward model and regularized Newton method. Finally we correct borehole effect on the apparent conductivity responses of two different models with the algorithm, and the results demonstrate the effectiveness of the algorithm.

1. Kriegshauser, B., O. Fanini, S. Forgang, G. Itskovich, M. Rabinovich, et al. "A new multicomponent induction loggingtool to resolve anisotropic formations," SPWLA 40th Ann. Log. Symp., 2000. Google Scholar

2. Zhdanov, M. S., D. Kennedy, and E. Peksen, "Foundation of the tensor induction well logging," Perophysics, Vol. 42, No. 42, 588-610, 2001. Google Scholar

3. Zhdanov, M. S., W. D. Kennedy, A. B. Cheryauka, and E. Peksen, "Principles of tensor induction well logging in a deviated well in an anisotropic medium," SPWLA 42th Ann. Log. Symp., June 17-20 2001. Google Scholar

4. Wang, T., L. Yu, and F. Otto, "Multicomponent induction response in a borehole environment," Geophysics, Vol. 68, No. 5, 1510-1518, 2003.
doi:10.1190/1.1620624 Google Scholar

5. Wang, T. and S. Fang, "3-D electromagnetic anisotropy modeling using finite differences," Geophysics, Vol. 66, No. 6, 1386-1398, 2001.
doi:10.1190/1.1486779 Google Scholar

6. Shen, J. S., "Modeling of the multi-component induction log in anisotropic medium by using finite difference method," Progress In Geophysics of China, Vol. 19, No. 1, 101-107, 2004. Google Scholar

7. Sun, X. Y. and Z. P. Nie, "Vector finite element analysis of multicomponent induction response in anisotropic formations," Progress In Electromagnetics Research, Vol. 81, 21-39, 2008.
doi:10.2528/PIER07121502 Google Scholar

8. Sun, X. Y., Z. P. Nie, A. Y. Li, and L. Xi, "Numerical modeling of multicomponent induction response in planar layered anisotropic formation," Chinese Geophysics. Google Scholar

9. Shen, J. S., "Modeling of the 3-D electromagnetic responses to the anisotropic medium by the edge finite element method," Well Logging Technology of China, Vol. 28, 11-15, Feb. 2004. Google Scholar

10. Everett, M. E., E. A. Badea, L. C. Shen, G. A. Merchant, and C. J. Weiss, "3-D finite element analysis of induction logging in a dipping formation," IEEE Trans. Geoscience and Remote Sensing, Vol. 39, 2244-2252, October 2003.
doi:10.1109/36.957287 Google Scholar

11. Michalski, K. A. and J. R. Mosing, "Multilayered media Green's functions in integral formulations," IEEE Trans. on Antennas and Propagation, Vol. 45, No. 3, 508-519, 1997.
doi:10.1109/8.558666 Google Scholar

12. Svezhentsev, A. Y., "Mixed-potential Green's function of an axially symmetric sheet magnetic current on a circular cylindrical metal surface," Progress In Electromagnetics Research, Vol. 60, 245-264, 2006.
doi:10.2528/PIER05070203 Google Scholar

13. Eroglu, A. and J. K. Lee, "Dyadic Green's functions for an electrically gyrotropic medium," Progress In Electromagnetics Research, Vol. 58, 223-241, 2006.
doi:10.2528/PIER05070203 Google Scholar

14. Sun, J., C.-F. Wang, L.-W. Li, and M.-S. Leong, "Mixed potential spatial domain Green's functions in fast computational form for cylindrically stratified media," Progress In Electromagnetics Research, Vol. 45, 223-241, 2006.
doi:10.2528/PIER03020201 Google Scholar

15. Li, L.-W., N.-H. Lim, W.-Y. Yin, and J.-A. Kong, "Eigenfunctional expansion of dyadic Green's functions in gyrotropic media using cylindrical vector wave functions," Progress In Electromagnetics Research, Vol. 43, 101-121, 2003.
doi:10.2528/PIER04070201 Google Scholar

16. Gao, G., C. Torres-Verdin, and T. M. Habashy, "Analytical techniques to evaluate the integrals of 3D and 2D spatial dyadic Green's functions," Progress In Electromagnetics Research, Vol. 52, 47-80, 2005.
doi:10.2528/PIER04070201 Google Scholar

17. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, 1990.

18. Wang, H., P. So, S. Yang, and W. J. R. Hoefer, "Numerical modeling of multicomponent induction well-logging tools in the cylindrically stratified anisotropic media," IEEE Trans. Geoscience and Remote Sensing, Vol. 46, No. 4, 1134-1147, April 2008.
doi:10.1109/TGRS.2008.915748 Google Scholar

19. Barber, T., B. Anderson, and A. Abubakar, "Determining formation resistivity anisotropy in the presence of invasion," SPE Annual Technical Conference and Exhibition Held in Houston, September 2004. Google Scholar

20. Habashy, T. M. and A. Abubakar, "A general framework for constraint minimization for the inversion of electromagnetic measurements," Progress In Electromagnetics Research, Vol. 46, 265-312, 2004.
doi:10.2528/PIER03100702 Google Scholar

21. Avdeev, D. B. and A. D. Avdeeva, "A rigorous three-dimensional magnetotelluric inversion," Progress In Electromagnetics Research, Vol. 62, 41-48, 2006.
doi:10.2528/PIER06041205 Google Scholar

22. Abubakar, A., T. M. Habashy, and P. M. Van den Berg, "Nonlinear inversion of multi-frequency microwave fresnel data using the multiplicative regularized contrast source inversion," Progress In Electromagnetics Research, Vol. 62, 193-201, 2006.
doi:10.2528/PIER06042205 Google Scholar

23. Pingenot, J., "Full wave analysis of signal attenuation in a lossy rough surface cave using a high order time domain vector finite element method," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 12, 1695-1705, 2006.
doi:10.1163/156939306779292408 Google Scholar

24. Hernandez-Lopez, M. A. and M. Quintillan-Gonzalez, "A finite element method code to analyse waveguide dispersion," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 397-408, 2007.
doi:10.1163/156939307779367396 Google Scholar

Dr. Xiangyang Sun

Professor Zai-Ping Nie

Dr. Aiyong Li

Dr. Xi Luo