Modeling of acoustoelastic borehole waves subjected to tectonic stress with formation anisotropy and borehole deviation

Sonic logging is a promising technique to estimate tectonic stress around a borehole. The key to successful evaluation of tectonic stress is having a thorough understanding of forward model which implies responses of borehole waves to tectonic stress. We propose a generic model to simulate responses of borehole waves to tectonic stress based on semi-analytical finite element method and acoustoelasticity. This model can compute distribution of tectonic stress around an inclined borehole with arbitrary anisotropic formation and simulate acoustoelasticities of borehole waves under this complicated stress. To avoid tedious and time consuming code development, we also provide an easy access to the model by reformulating and implementing the governing equations in a commercial software package. We validate the model by using three case studies where analytical/numerical solutions are available, showing good agreements between the results from our model and solutions in the literature. We then apply the model to some important applications in boreholes, demonstrating that this model can provide a powerful tool for understanding of responses of borehole waves to tectonic stress.

Gaussian beam imaging of fractures near the wellbore using sonic logging tools after removing dispersive borehole waves

The ability to image near-wellbore fractures is critical for wellbore integrity monitoring as well as for energy production and waste disposal. Single-well imaging uses a sonic logging instrument consisting of a source and a receiver array to image geologic structures around a wellbore. We use cross-dipole sources because they can excite waves that can be used to image structures farther away from the wellbore than traditional monopole sources. However, the cross-dipole source also will excite large-amplitude, slowly propagating dispersive waves along the surface of the borehole. These waves will interfere with the formation reflection events. We have adopted a new fracture imaging procedure using sonic data. We first remove the strong amplitude borehole waves using a new nonlinear signal comparison method. We then apply Gaussian beam migration to obtain high-resolution images of the fractures. To verify our method, we first test our method on synthetic data sets modeled using a finite-difference approach. We then validate our method on a field data set collected from a fractured natural gas production well. We are able to obtain high-quality images of the fractures using Gaussian beam migration compared with Kirchhoff migration for the synthetic and field data sets. We also found that a low-frequency source (around 1 kHz) is needed to obtain a sharp image of the fracture because high-frequency wavefields can interact strongly with the fluid-filled borehole.

A theoretical study on formation shear radial profiling in well-bonded cased boreholes using sonic dispersion data based on a parameterized perturbation model

Interpretation of sonic data can be challenging in the presence of a steel casing that has a strong influence on elastic waves propagating along a borehole. The cement annulus behind the casing together with drilling-induced near-wellbore alteration causes radial heterogeneity in the propagating medium. It is necessary to study the influence of such heterogeneities on borehole waves and estimate the radial extent of near-wellbore alteration in terms of radial variation of velocities away from the casing. To this end, we based our study on the model of a fluid-filled well-bonded cased borehole surrounded by a cylindrically layered formation. The formation is isotropic and purely elastic, and can be either fast or slow. Borehole monopole and dipole dispersions for this kind of model can be obtained from a root finding mode-search routine. A modified perturbation model based on Hamilton’s principle is used to predict changes in borehole dispersions caused by formation heterogeneities. A two-layer formation model as the reference state is introduced, which always provides normal dispersive reference dispersion for calculations of perturbation integrals for fast and slow formations. Radial variations of the formation shear velocity can be expressed in terms of a parametric exponential profile. Consequently, estimation of these parameters in the assumed profile yields the radial variation of the formation shear slowness away from the casing. Numerical results using synthetic examples are presented to demonstrate the validity of this radial profiling methodology.