Chaur-Jian Hsu

MANDREL EFFECTS ON THE DIPOLE FLEXURAL MODE IN A BOREHOLE

The flexural mode is the lowest-order borehole mode with dipole excitation. The low-frequency asymptote of the flexural wave speed is used to estimate the formation shear speed in well logging. The borehole flexural mode measurement system consists of a mandrel that holds the transmitter and an array of receivers. This mandrel is, generally, designed to minimize the interference between any mandrel and the borehole flexural modes. A slotted sleeve housing that makes the sleeve arrival significantly slower than the formation arrival enables the processing of the recorded waveforms based on a model of fluid-filled boreholes without any mandrel. The objective of this work is to investigate the basic physics of mandrel effects on borehole flexural mode for the condition that the mandrel is in the form of a rod or pipe that is not necessarily slower than the formation arrivals. To this end, we describe an experimental and theoretical study of flexural modes in a borehole with a concentric mandrel and water ann...

Tube waves and mandrel modes: Experiment and theory

The characteristics of tube waves in a borehole, with and without a solid cylindrical mandrel, which may be either elastic or poro-elastic, are compared. With an elastic mandrel, the tube waves are slower, more dispersive, and more sensitive to the formation shear modulus than without. Similarly extensional mode characteristics are compared in the presence of a formation. In the presence of an elastic formation the extensional mode is faster, more dispersive than without, and it is only slightly sensitive to the formation shear properties. These calculated characteristics are in excellent agreement with our measured data. Additionally, the characteristics of tube waves and extensional modes are studied in a borehole in the presence of a concentric liquid-saturated porous mandrel whose acoustic properties are calculated using the Biot theory. The coupling of the tube wave propagating in the annulus with the slow wave propagating in the porous mandrel introduces attenuation and additional dispersion to the ...

Experiments on stress dependent borehole acoustic waves

In the laboratory setup, a borehole traverses a dry sandstone formation, which is subjected to a controlled uniaxial stress in the direction perpendicular to the borehole axis. Measurements are made in a single loading-unloading stress cycle from zero to 10 MPa and then back down to zero stress. The applied stress and the presence of the borehole induce anisotropy in the bulk of the material and stress concentration around the borehole, both azimuthally and radially. Acoustic waves are generated and detected in the water-filled borehole, including compressional and shear headwaves, as well as modes of monopole, dipole, quadrupole, and higher order azimuthal symmetries. The linear and non-linear elastic parameters of the formation material are independently quantified, and utilized in conjunction with elastic theories to predict the characteristics of various borehole waves at zero and finite stress conditions. For example, an analytic theory is developed which is successfully used to estimate the changes of monopole tube mode at low frequency resulted from uniaxial stress, utilizing the measured material third order elasticity parameters. Comparisons between various measurements as well as that between experiments and theories are also presented.

Effect of granular media on the vibrational response of a resonant structure: Theory and experiment

The acoustic response of a structure that contains a cavity filled with a loose granular material is analyzed. The inputs to the theory are the effective masses of each subsystem: that of the empty-cavity resonating structure and that of the granular medium within the cavity. This theory accurately predicts the frequencies, widths, and relative amplitudes of the various flexural mode resonances observed with rectangular bars, each having a cavity filled with loose tungsten granules. Inasmuch as the dominant mechanism for damping is due to adsorbed water at the grain-grain contacts, the significant effects of humidity on both the effective mass of the granular medium as well as on the response of the grain-loaded bars are monitored. Here, depending upon the humidity and the preparation protocol, it is possible to observe one, two, or three distinct resonances in a wide frequency range (1-5 kHz) over which the empty bar has but one resonance. These effects are understood in terms of the theoretical framework, which may simplify in terms of perturbation theories.

Borehole dipole and quadrupole modes in anisotropic formations

Sonic measurements while drilling are made in the presence of a drill collar (in the form of a thick steel pipe) that provides an additional path for the acoustic energy propagating from the transmitter to an array of receivers. Low-frequency asymptotes of both dipole and quadrupole modes yield the formation far-field shear slowness. Intrinsic or stress-induced anisotropy of surrounding formation in a vertical well is generally investigated by a wireline sonic tool using a borehole dipole mode that exhibits cos/spl theta/ azimuthal dependence in their associated acoustic field propagating along the borehole axis. The fast and slow dipole shear polarizations are orthogonal to one another in the presence of any azimuthal anisotropy. The two flexural modes are excited by rotating the dipole transmitter by 90/spl deg/ from one of the primary shear polarization directions. However, borehole quadrupole modes appear to be more promising for estimating the far-field formation shear slowness in the presence of a drill collar. Formation anisotropy can also be investigated using such quadrupole modes that exhibit cos2/spl theta/ azimuthal dependence in their acoustic field propagating along the borehole axis. The two canonical quadrupole modes are excited by rotating the quadrupole transmitter by 45/spl deg/ from one of the primary shear polarization directions. Borehole flexural dispersions exhibit a crossover in the presence of a uniaxial stress in a plane perpendicular to the borehole axis. In contrast, a perturbation analysis of quadrupole modes in the presence of a uniaxial stress does not show any such crossovers. Both the orthogonal quadrupole modes corresponding to the transmitter oriented parallel and 45/spl deg/ to the uniaxial stress direction asymptote to the same shear slowness at low frequencies. This shear slowness is essentially the same as the fast shear slowness measured by a dipole transmitter parallel to the uniaxial stress direction. However, there are increasing differences between the two orthogonal quadrupole mode slownesses at higher frequencies. Quadrupole waves with positive polarization parallel to the uniaxial stress direction always exhibit larger slownesses than those polarized 45/spl deg/ to the uniaxial stress direction. Even though stress-induced anisotropy in shear slownesses at very low frequencies is not predicted the orthogonal quadrupole modes, significant differences at higher frequencies can be used as an indicator of stress-induced anisotropy magnified by the near-wellbore stress concentrations.

Mandrel effects on tube waves

The characteristics of tube waves in water‐filled boreholes with and without an elastic cylindrical mandrel in the borehole are compared. With a mandrel, the tube waves are slower, more dispersive, and more sensitive to the formation shear modulus than without. Additionally, the characteristics of tube waves in a borehole in the presence of a liquid‐saturated porous mandrel were also studied. The tube waves propagating in the annulus couple with the slow waves propagating in the porous mandrel. This coupling and the viscous dissipation of the slow waves introduce attenuation and additional dispersion to the tube waves. Whether the mandrel is porous or not, there are two modes which are weakly dispersive in the quasistatic limit. Very roughly, the two modes consist of an extensional mode in the rod and a fluid‐based mode in the annulus which are coupled together.

Interaction of flexural modes of a borehole and a cylinder

A low‐frequency dipole source excites flexural waves in cylindrical structures. Flexural waves in rods and pipes assume vanishingly small phase velocities at low frequencies. On the other hand, the flexural waves of a borehole surrounded by an infinite formation asymptotically approach formation shear wave velocity at low frequencies. These two individual lowest‐order flexural modes interact with each other in a composite structure where a rod or pipe is concentrically placed in a borehole surrounded by an infinite formation with liquid in the annulus. This interaction results in two coupled modes of the composite structure. Depending on how strong this interaction is, these two coupled modes may resemble or drastically differ from the two individual modes of the rod (or pipe) as well as the borehole. The interaction is stronger at frequencies where the two individual modes are closer in phase velocity. Results of experimental and theoretical studies will be reviewed and compared.