Effects of collar eccentricity on azimuthal response characteristics for acoustic reflection measurement while drilling

Abstract

Acoustic reflection imaging has been successfully applied in postdrilling wireline logging, and the technique is potentially more valuable in acoustic logging while drilling (ALWD), particularly in geosteering while drilling. Because of the common occurrence of tool eccentering in drilling, the impact of drill collar eccentricity on the acoustic wavefield inside and outside the borehole must be considered. Therefore, we analyze the effect of an eccentric drill collar on acoustic reflection imaging while drilling using analytical solutions in a dual-cylindrical coordinate system. The virtual source analogy and the translational addition theorem for cylindrical Bessel functions are used to calculate the response of the fluid-filled borehole with an eccentric collar to the incident wavefield from a formation reflector. The analysis results are validated with those from 3D finite-difference simulations. We also have studied the azimuthal variation of the received wavefield and compared the results with their centralized counterparts, for which the effects of collar eccentricity, frequency of the source, and formation elastic property are analyzed. The results indicate that the asymmetric feature of the wavefield due to the eccentric collar allows for determining the azimuth of the reflector, providing a solution to the azimuth ambiguity problem of borehole acoustic reflection imaging. Our results, besides developing an effective method for eccentric collar ALWD modeling, can be used to provide a theoretical foundation for ALWD tool development and data interpretation.