Mode Waves In A Fluid-Filled Borehole Embedded In A Porous Formation

Acoustic logging is a general method in oil and gas exploration. Especially, it is important to analyze the wave components in full wave logging. Studying the problems on mode waves propagating in a cylindrical borehole embedded in fluid-saturated poroelastic formation is necessary.First of all, the paper indicates characteristic of seepage while the waves propagates in poroelastic formation, and emphasize the meaning of additional mass and of dynamic permeability.The next step is to found the model of a cylindrically layered borehole embedded in poroelastic media. After bringing forward the single-valued definition of the characteristic function and selecting the integral contour, the distribution of poles on frequency-complex wave number domain is completely presented, based on which we can analyze the dispersion and the attenuation of normal mode waves and leaky mode waves. It is learned that normal mode and leaky mode have completely different reasons of attenuation. The former is caused by relative motion between fluid phase and solid phase while the latter is caused by geometry characteristic of the borehole.Furthermore, by calculating the pole residue we get the excitation intensity of corresponding mode waves, and then get the time-domain waveforms by FFT. Afterward, the influence of waveforms affected by source center frequency is discussed. Superposing all waveforms of mode waves and waveforms calculated by branch cut integral finally get the full waveform. It shows velocity and contribution of each wave component.At last, the influence of permeability and of shear modulus to velocity and attenuation of Stoneley waves is studied. We find that with different permeability and modulus, the velocity and attenuation of Stoneley waves are affected. This conclusion can provide theoretical basis of estimating the parameters of strata by Stoneley waves.