A finite difference modeling of acoustic wave field in the near-borehole formation excited by an arcuate source

We propose an acoustic logging-while-drilling (LWD) arcuate source, aiming to develop a three-dimensional acoustic reflection LWD tool, which is able to accurately locate tile reflectors outside of the fluid-filled borehole. The paper examines the acoustic field produced by the arcuate source under complex borehole conditions (collar eccentricity, anisotropic formations and irregular borehole), and discusses the influence factors of the method. Numerical results show that, the source is able to produce compressional wave field of good azimuthal resolution for most cases. In a circular borehole, the source is able to directional radiate compressional waves regardless of that the formation is fast or slow, and the directivity pattern of the compressional wave field includes a main lobe with a narrow 3 dB angle width and side lobes of low level. It suggests that the source is suitable for acoustic reflection LWD. The factors, including the formation anisotropy and the roughness of borehole sidewall, have little influence on the azimuthal characteristic of the compressional wave field. The tool eccentricity and the wellbore sidewall damage caused by the drilling operation greatly affect the compressional wave field. The acoustic field is of good azimuthal resolution when the damage depth is less than 3 cm and the eccentric distance l < 2 cm, whereas several side lobes of high degree appear in the radiation pattern when the damage depth is larger than 6 cm. The presented results provide necessary theoretical fundamentals for the development of the three-dimensional acoustic reflection LWD tool.