Simulations Of Acoustic Logs In Transversely Isotropic Formations And Researches On Permeability Inversion

Acoustic logging is a useful method of geophysical measurements and explorations for oil or gas reservoirs. To develop the logging technique and extract reservoir informations, researches on cylindrical elastic-wave propagation along a radially layered medium is of great practical importance. Transverse isotropy (TI) of sedimentary rocks is a typical characteristic in the lithospere medium. In the present thesis, full waves and component waves excited by a multipole source in a borehole is simulated by the analytical and numerical methods. The inversion scheme for formation permeabilities is put forward after studying the influence of each factor on the wave field.The wavefields in a vertically extending wellbore are modeled first. In this case, the bore axis is parallel to the TI symmetry axis and the wave equations inside and outside the borehole can therefore be analytically solved. The dispersion of the guided waves can be investigated by finding poles of the borehole acoustic function. Previous works have taken for granted that guided-wave velocities of the pseudo-Rayleigh, flexural, and screw modes equal the shear speed at the low-frequency limits in TI media without proof. With the results of wavefield computations, however, it is revealed that if parameters of a TI formation satisfyδ>ε+c₄₄/2c₃₃, asymptotic velocities of those guided waves are lower than the shear speed, where c₃₃ and c₄₄ are the moduli related to the compressional and shear wave along the TI symmetry axis, respectively, andεandδare the anisotropic coefficients. The simulated full-waves further show that in such a kind of formations, the measurement result of shear speed obtained from those guided-wave arrivals are always smaller than the true value.Borehole wavefields in a fluid-saturated porous TI formation excited by a monopole source is then simulated. The dispersion, attenuation, and excitation of all modes, including the unleaky and leaky modes, are investigated. It is revealed that the attenuation of the unleaky modes is caused by the relative motion between the porous skeleton and the viscous pore-fluid while that of the leaky modes includes both the intrinsic dissipation and the geometric leak of mechanical energy. Hence the leaky modes, whose velocities are higher than the shear speed, attenuate rapidly as they propagate. Based on the simulation results of component waves, influences of all parameters on the guided waves as well as the critical refracted waves are investigated. Sensitivity analysis theoretically confirms that Stoneley wave can be used to measure the permeability and the shear modulus on the horizontal plane. In the numerical example, those two parameters are well extracted from Stoneley waveforms in the time-domain by solving a nonlinear least-squares problem. It is shown that the initial estimations of the porosity and the vertical permeability have little effect on the inversion results.The borehole, however, is not parallel to the TI symmetry axis in most cases. Dipole acoustic waves in such a borehole are computed by a 3-D finite-difference time-domain (FDTD) algorithm instead of the analytical method. Due to the shear anisotropy, a dipole source can excite a fast and a slow flexural mode if the bore axis deviates from the TI symmetry axis. That is the flexural-wave splitting phenomenon. The dipole orientation has no relation with the velocities or phases of flexural waves. It influences the relative amplitudes of the two modes. In most situations, the fast and slow flexural modes in the low-frequency range travel at the speeds of the fast and slow shear wave, respectively. The numerical results show that even in the formations withδ>ε+c₄₄/2c₃₃, extracting the shear velocities from the flexural arrivals is still possible if the borehole deviation is large enough. Moreover, the wavefields in gradient heterogeneous or horizontally layered formations are also modeled by the FDTD code.For a permeability anisotropic porous model, once the principal direction of the TI permeability tensor is not consistent with the coordinate axis, all velocity components of pore-fluid flow are coupled together. And the equations of generalized Darcy's law cannot be discretized using the conventional stress-velocity staggered grids. To solve such a problem, the modified FDTD algorithm is introduced to rewrite Darcy's equations into the finite-difference formulations. Thus the dipole wavefields in a borehole deviated from the TI symmetry axis can be simulated. According to our numerical examples, it is concluded that the distributing plane of directed cracks can be detected from the attenuation and the amplitudes of flexural-wave signals at the cross dipole array of receivers. Based on the results of sensitivity analysis, it is found that the flexural attenuation can be used to measure the formation permeability. In a vertical well, the horizontal permeability can be obtained, but the inversion accuracy depends on the precision of the porosity and vertical-permeability estimation. So the inversion stability is worse compared with the Stoneley-wave inversion process. In a horizontal well, the flexural wave excited by a horizontally polarized dipole can be used to extract the horizontal permeability; while the vertical permeability can be measured from the flexural attenuation generated by the vertically oriented source. The measurement results of permeabilities are very close to the true values in a highly permeable formation. The inversion accuracy, however, is obviously influenced by the anisotropy level if the formation permeability is lower in a horizontal borehole. The stronger the permeability anisotropy is, the worse the measurement precision is. On the basis of the inversion examples, an effective method is provided to estimate the anisotropic permeabilities from the log data of a cross-dipole sonic tool.