Various methods have been developed in ExxonMobil for accurate evaluation of anisotropic rock properties from well logs. Firstly, a method based on the full Biot's poro-elastic theory was proposed to estimate the shear-wave anisotropy (?) from monopole Stoneley waves. The method was applied to a deep-water West Africa well and observed promising results. Secondly, ExxonMobil's Anisotropic Micro-Porosity Model was utilized to predict the anisotropy (Thomsen) parameters in vertically transverse isotropic (VTI) media from a standard suite of well logs. The model addresses both shale anisotropy and stress-induced anisotropy simultaneously. Application of the model to many vertical and highly deviated wells around the world has resulted in significant improvements in the predicted Vp/Vs and well-to-seismic gather ties. Thirdly, we proposed methodologies to infer formation stress orientation and magnitude from the azimuthal anisotropy information extracted from borehole sonic waveform data.
Sedimentary rocks exhibit anisotropic behavior at all scales. Recent publications show very strong elastic and transport property anisotropy in shaly formations. It is commonly accepted that shale anisotropy has the symmetry of VTI, as indicated by the fact that cross-dipole logs show virtually no azimuthal anisotropy in shales.
Stress-induced anisotropy has been studied in the laboratory by many authors. Nur and Simmons (1969) conducted a uniaxial stress experiment on a cylindrical dry granite sample to investigate the effect of stress-induced crack alignment on wave velocities. Yin (1992) investigated the same effect by testing various rock samples, ranging from unconsolidated sands to consolidated rocks, from synthetic to real samples, using a true triaxial system. P-wave and two orthogonally polarized S-wave velocities were measured in three principal directions, giving a total of 9 measurements at each given stress condition. Yin's results show that Vp/Vs in the major principal stress direction is significantly higher than that in the minor principal stress directions. This important observation explains the observed abnormally high Vp/Vs ratios in shallow unconsolidated sands from many West African wells.
There are, in general, two types of stress-induced anisotropy in unconsolidated sands. In a tectonically passive sedimentary basin, the vertical effective stress is typically much higher than the two horizontal effective stresses whereas the two horizontal stresses are more or less the same. Typically this will result in polar anisotropy (VTI) in the reservoir rocks. In a more general case where the two horizontal stresses are also different, the reservoir rocks will exhibit orthorhombic symmetry (with both polar anisotropy and azimuthal anisotropy). In vertical wells, azimuthal anisotropy can be measured from cross-dipole logs. In this paper, the azimuthal anisotropy will be used to determine the maximum and minimum horizontal stresses.
The anisotropic behavior of a VTI medium can be quantified using the three Thomsen parameters ?, ? and ?, defined as follows (Thomsen 1986).
(Mathematical equations (1), (2) and (3) available in full paper.)
Here, Cij is the elastic tensor of the VTI medium. The quantity e approximately measures the P-wave anisotropy, i.e. the relative change between P-wave velocity in the fast direction and that in slow direction.
