Ge Gabriel Chao

Guided wave modes in porous cylinders: Experimental results

In this paper guided wave modes in porous media are investigated. A water-saturated porous cylinder is mounted in the test section of a shock tube. Between the porous sample and the wall of the shock tube a water-filled annulus exists. For very small annulus width, bulk waves are generated and one-dimensional modeling is sufficient. Otherwise two-dimensional effects become important and multiple guided wave modes occur. Using a newly developed traversable positioning system in the shock tube, the frequency-dependent phase velocities and damping coefficients in the 1-120 kHz frequency range were measured. Pronys method was used for data processing. Agreement was found between the experimental data and the two-dimensional modeling of the shock tube which was based on Biots theory.

Shock-induced borehole waves in porous formations: Theory and experiments

The characteristics of the pseudo-Stoneley wave along boreholes in porous formations are studied in a broad band of frequencies (100 Hz–200 kHz). Experiments are performed using a shock tube technique to excite the pseudo-Stoneley wave in a water saturated confined reservoir. The formation is a natural Berea sandstone. Frequency-dependent phase velocities and damping coefficients are measured using this technique. Quantitative agreement between the experimental results and the theoretical predictions is found for the phase velocity in the frequency range from 10 to 50 kHz. Theoretically, the influence of the permeability on the phase velocity, attenuation, radial displacement, and pore pressure is studied on the basis of the Biot theory and the contribution of the different bulk modes to the average radial displacement is analyzed in the frequency domain. The numerical results indicate that the permeability dependence at low frequencies is caused by the Biot slow wave.

Dispersive surface waves along partially saturated porous media

Numerical results for the velocity and attenuation of surface wave modes in fully permeable liquid/partially saturated porous solid plane interfaces are reported in a broadband of frequencies (100?Hz–1?MHz). A modified Biot theory of poromechanics is implemented which takes into account the interaction between the gas bubbles and both the liquid and the solid phases of the porous material through acoustic radiation and viscous and thermal dissipation. This model was previously verified by shock wave experiments. In the present paper this formulation is extended to account for grain compressibility. The dependence of the frequency-dependent velocities and attenuation coefficients of the surface modes on the gas saturation is studied. The results show a significant dependence of the velocities and attenuation of the pseudo-Stoneley wave and the pseudo-Rayleigh wave on the liquid saturation in the pores. Maximum values in the attenuation coefficient of the pseudo-Stoneley wave are obtained in the 10–20?kHz range of frequencies. The attenuation value and the characteristic frequency of this maximum depend on the liquid saturation. In the high-frequency limit, a transition is found between the pseudo-Stoneley wave and a true Stoneley mode. This transition occurs at a typical saturation below which the slow compressional wave propagates faster than the pseudo-Stoneley wave.

Guided wave modes in porous cylinders: Theory

The classical theory of wave propagation in elastic cylinders is extended to poro-elastic mandrel modes. The classical theory predicts the existence of undamped L modes and damped C, I, and Z modes. These waves also appear in poro-elastic mandrels, but all of them become damped because of viscous effects. The presence of the Biot slow bulk wave in the poro-elastic material is responsible for the generation of additional mandrel modes. One of them was already discussed by Feng and Johnson, and the others can be grouped together as so-called D modes. The damping of these D modes is at least as high as the damping of the free-field slow wave.

Measurements of shock-induced guided and surface acoustic waves along boreholes in poroelastic materials

Acoustic experiments on the propagation of guided waves along water-filled boreholes in water-saturated porous materials are reported. The experiments were conducted using a shock tube technique. An acoustic funnel structure was placed inside the tube just above the sample in order to enhance the excitation of the surface modes. A fast Fourier transform-Prony-spectral ratio method is implemented to transform the data from the time-space domain to the frequency-wave-number domain. Frequency-dependent phase velocities and attenuation coefficients were measured using this technique. The results for a Berea sandstone material show a clear excitation of the fundamental surface mode, the pseudo-Stoneley wave. The comparison of the experimental results with numerical predictions based on Biot’s theory of poromechanics [ J. Acoust. Soc. Am. 28, 168 (1956) ], shows that the oscillating fluid flow at the borehole wall is the dominant loss mechanism governing the pseudo-Stoneley wave and it is properly described by the Biot’s model at frequencies below 40?kHz. At higher frequencies, a systematic underestimation of the theoretical predictions is found, which can be attributed to the existence of other losses mechanisms neglected in the Biot formulation. Higher-order guided modes associated with the compressional wave in the porous formation and the cylindrical geometry of the shock tube were excited, and detailed information was obtained on the frequency-dependent phase velocity and attenuation in highly porous and permeable materials. The measured attenuation of the guided wave associated with the compressional wave reveals the presence of regular oscillatory patterns that can be attributed to radial resonances. This oscillatory behavior is also numerically predicted, although the measured attenuation values are one order of magnitude higher than the corresponding theoretical values. The phase velocities of the higher-order modes are generally well predicted by theory.

Seismic signatures of partial saturation on acoustic borehole modes

We present an exact theory of attenuation and dispersion of borehole Stoneley waves propagating along porous rocks containing spherical gas bubbles by using the Biot theory. An effective frequency-dependent fluid bulk modulus is introduced to describe the dynamic (oscillatory) behavior of the gas bubbles. The model includes viscous, thermal, and radiation damping. It is assumed that the gas pockets are larger than the pore size, but smaller than the wavelengths involved (mesoscopic inhomogeneity). A strong dependence of the attenuation of the Stoneley wave on gas fraction and bubble size is found. Attenuation increases with gas fraction over the complete range of studied frequencies (10 Hz–50 kHz). The dependence of the phase velocity on the gas fraction and bubble size is restricted to the lower frequency range. These results indicate that the interpretation of Stoneley wave properties for the determination of, for example, local permeability formation is not straightforward and could be influenced by the presence of gas in the near-wellbore zone. When mud-cake effects are included in the model, the same observations roughly hold, though dependence on the mud-cake stiffness is quite complex. In this case, a clear increase of the damping coefficient with saturation is predicted only at relatively high frequencies.

An experimental and theoretical study of shock-induced surface waves in porous boreholes

Surface wave modes in a water-filled borehole surrounded by a poroelastic medium are studied. Numerical and experimental results are presented for the dispersion relation of shock-induced surface waves in a borehole in a confined formation in a broad band of frequencies (1–50 kHz). Theoretically, it is shown that permeability affects considerably both the phase velocity and damping coefficient of the pseudo-Stoneley wave. Experimentally, a vertical shock tube is used to excite pseudo-Stoneley and pseudo-Rayleigh waves as well as the bulk compressional wave. Qualitative agreement between experiment and theory is obtained.