Effects of the outermost boundary on acoustic waves in an artificial cased borehole

Abstract

In this paper, we treat a 3-D cased borehole model, to investigate theoretically and numerically the effects of an outermost boundary on borehole waves, and to discuss borehole wave penetration in a radial direction. The closed form solution for this model, numerical estimates of full waveforms, and excitation spectra are presented. We show that, when the radius of the simulated formation is greater than 1.5 m, the outermost boundary has little influence on borehole waveforms, for source-receiver spacings between 1.0 m and 1.5 m and at typical logging frequencies. When the radius of the outermost boundary is less than 0.5 m the influence of the outermost boundary cannot be neglected. In order to absorb energy at the outermost boundary, a solid absorption material is better than a fluid one. Even if the first or second boundary is not cemented, the effect of the outermost boundary on borehole waveforms cannot be totally neglected in a typical sonic logging environment if the outermost boundary radius is less than 0.5 m. At low frequencies (for example, for a source centre frequency less than 3 kHz), these effects are negligible. The numerical analysis also illustrates that low-frequency mode waves, such as Stoneley waves in an open borehole, have a radial penetration less than 10 cm, which implies that formation information such as permeability determined by such mode waves is limited to a very shallow zone around the borehole.