Investigation of Effects of Large Dielectric Constants on Triaxial Induction Logs
ABSTRACT
The dielectric effect is receiving increasing interest in the study of resistivity logging. Several recent findings have proven that the dielectric effect can cause negative imaginary signals on the array induction logging. However, very few researches discuss the dielectric effect on the triaxial induction logging which is a novel technology in solving anisotropy problem. In this paper, we investigate the effect of large dielectric constants on a basic triaxial induction tool in a 1-D homogenous earth formation. The simulation model is derived from Maxwell equation and calculated by wave number integration. Sufficient simulations have been done. We performed an asymptotic analysis of the dielectric effect within the low-freq limit, yielding interesting observations on the dielectric effect with respect to frequency, spacing, and anisotropy. Those findings provide important and useful guidance for researchers to study on the dielectric effect on the triaxial induction logging.
The dielectric effect is receiving increasing interest in the study of resistivity logging. Several recent findings have proven that the dielectric effect can cause negative imaginary signals on the array induction logging. However, very few researches discuss the dielectric effect on the triaxial induction logging which is a novel technology in solving anisotropy problem. In this paper, we investigate the effect of large dielectric constants on a basic triaxial induction tool in a 1-D homogenous earth formation. The simulation model is derived from Maxwell equation and calculated by wave number integration. Sufficient simulations have been done. We performed an asymptotic analysis of the dielectric effect within the low-freq limit, yielding interesting observations on the dielectric effect with respect to frequency, spacing, and anisotropy. Those findings provide important and useful guidance for researchers to study on the dielectric effect on the triaxial induction logging.
Cite this paper
Z. Zhang, B. Yu and C. Liu, "Investigation of Effects of Large Dielectric Constants on Triaxial Induction Logs," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1811-1817. doi: 10.4236/am.2012.331246.
Z. Zhang, B. Yu and C. Liu, "Investigation of Effects of Large Dielectric Constants on Triaxial Induction Logs," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1811-1817. doi: 10.4236/am.2012.331246.
References
[1] R. J. Sengwa and A. Soni, “Low-Frequency Dielectric Dispersion and Microwave Dielectric Properties of Dry and Water-Saturated Limestones of the Jodhpur Region,” Geophysics, Vol. 71, No. 5, 2006, pp. G269-G277. doi:10.1190/1.2243743 [2] S. Ahualli, M. L. Jiménez and A. V. Delgado, “Electroacoustic and Dielectric Dispersion of Concentrated Colloidal Suspensions,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 13, No. 3, 2006, pp. 657-663. doi:10.1109/TDEI.2006.1657981 [3] R. H. Hardman and L. C. Shen, “Theory of Induction Sonde in Dipping Beds,” Geophysics, Vol. 51, No. 3, 1986, pp. 800-809. doi:10.1190/1.1442132 [4] M. B. McBRIDE, “A Critical of Diffuse Double Layer Models Applied to Colloid and Surface Chemistry,” Clays and Clay Minerals, Vol. 45, No. 4, 1997, pp. 598-608. [5] M. Luo and C. Liu, “Numerical Simulations of Large Dielectric Enhancement in Some Rocks,” Society of Geophysical Exploration, CPS/SEG Beijing 2009 Conference and Exposition, Beijing, 2009. [6] B. Anderson, T. Barber, and M. Luling, “Observations of Large Dielectric Effects on Induction Logs, or Can Source Rocks Be Detected with Induction Measurements,” Society of Professional Well Log Analysts Publications, Symposium Transactions, Veracruz, 4-7 June 2006. [7] B. Anderson, T. Barber, M. Luling, J. Rasmus and P. Sen, “Observations of Large Dielectric Effects on LWD Propagation-Resistivity Logs,” Symposium Transactions on Society of Professional Well Log Analysts Publications, Austin, 3-6 June 2007. [8] Z. Zhang, L. Yu, B. Kriegshauser and L. Tabarovasky, “Determination of Relative Angles and Anisotropic Resistivity Using Multicomponent Induction Logging Data,” Geophysics, Vol. 69, No. 4, 2004, pp. 898-908. doi:10.1190/1.1778233 [9] B. I. Anderson, T. D. Barber and T. M. Habashy, “The Interpretation and Inversion of Fully Triaxial Induction Data: A Sensitivity Study,” Transactions of the SPWLA 25th Annual Logging Symposium, Oiso, 1-13 June 2002. [10] B. Krieghauser, O. Fanini, S. Forgang, G. Itskovich, M. Rabinovich, L. Tabarovsy, L. Yu, M. Epov, P. Gupta and J. V. D. Horst, “A New Multicomponent Induction Logging Tool to Resolve Anisotropic Formations,” Transactions SPWLA 41st Annual Logging Symposium, Dallas, 4-7 June 2000. [11] G. S. Liu, F. L. Teixeira and G. J. Zhang, “Analysis of Directional Logging Sensors,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 3, 2010, pp. 1151-1158. [12] J. H. Moran and K. S. Kunz, “Basic Theory of Induction Logging and Application to Study of Two-Coil Sondes,” Geophysics, Vol. 27, No. 6, 1962, pp. 829-858. doi:10.1190/1.1439108 [13] L. Zhong, J. Li, A. Bhardwaj, L. C. Shen and R. C. Liu, “Computation of Triaxial Induction Logging Tools in Layered Anisotropic Dipping Formations,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 46, No. 4, 2008, pp. 1148-1163. doi:10.1109/TGRS.2008.915749
[1] R. J. Sengwa and A. Soni, “Low-Frequency Dielectric Dispersion and Microwave Dielectric Properties of Dry and Water-Saturated Limestones of the Jodhpur Region,” Geophysics, Vol. 71, No. 5, 2006, pp. G269-G277. doi:10.1190/1.2243743 [2] S. Ahualli, M. L. Jiménez and A. V. Delgado, “Electroacoustic and Dielectric Dispersion of Concentrated Colloidal Suspensions,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 13, No. 3, 2006, pp. 657-663. doi:10.1109/TDEI.2006.1657981 [3] R. H. Hardman and L. C. Shen, “Theory of Induction Sonde in Dipping Beds,” Geophysics, Vol. 51, No. 3, 1986, pp. 800-809. doi:10.1190/1.1442132 [4] M. B. McBRIDE, “A Critical of Diffuse Double Layer Models Applied to Colloid and Surface Chemistry,” Clays and Clay Minerals, Vol. 45, No. 4, 1997, pp. 598-608. [5] M. Luo and C. Liu, “Numerical Simulations of Large Dielectric Enhancement in Some Rocks,” Society of Geophysical Exploration, CPS/SEG Beijing 2009 Conference and Exposition, Beijing, 2009. [6] B. Anderson, T. Barber, and M. Luling, “Observations of Large Dielectric Effects on Induction Logs, or Can Source Rocks Be Detected with Induction Measurements,” Society of Professional Well Log Analysts Publications, Symposium Transactions, Veracruz, 4-7 June 2006. [7] B. Anderson, T. Barber, M. Luling, J. Rasmus and P. Sen, “Observations of Large Dielectric Effects on LWD Propagation-Resistivity Logs,” Symposium Transactions on Society of Professional Well Log Analysts Publications, Austin, 3-6 June 2007. [8] Z. Zhang, L. Yu, B. Kriegshauser and L. Tabarovasky, “Determination of Relative Angles and Anisotropic Resistivity Using Multicomponent Induction Logging Data,” Geophysics, Vol. 69, No. 4, 2004, pp. 898-908. doi:10.1190/1.1778233 [9] B. I. Anderson, T. D. Barber and T. M. Habashy, “The Interpretation and Inversion of Fully Triaxial Induction Data: A Sensitivity Study,” Transactions of the SPWLA 25th Annual Logging Symposium, Oiso, 1-13 June 2002. [10] B. Krieghauser, O. Fanini, S. Forgang, G. Itskovich, M. Rabinovich, L. Tabarovsy, L. Yu, M. Epov, P. Gupta and J. V. D. Horst, “A New Multicomponent Induction Logging Tool to Resolve Anisotropic Formations,” Transactions SPWLA 41st Annual Logging Symposium, Dallas, 4-7 June 2000. [11] G. S. Liu, F. L. Teixeira and G. J. Zhang, “Analysis of Directional Logging Sensors,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 3, 2010, pp. 1151-1158. [12] J. H. Moran and K. S. Kunz, “Basic Theory of Induction Logging and Application to Study of Two-Coil Sondes,” Geophysics, Vol. 27, No. 6, 1962, pp. 829-858. doi:10.1190/1.1439108 [13] L. Zhong, J. Li, A. Bhardwaj, L. C. Shen and R. C. Liu, “Computation of Triaxial Induction Logging Tools in Layered Anisotropic Dipping Formations,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 46, No. 4, 2008, pp. 1148-1163. doi:10.1109/TGRS.2008.915749