Theory And Application Of Sonic Velocity Logging In Anisotropic Formations

The anisotropy analysis and fracture/crack evaluation have long been important topics for the exploration and development of complex reservoirs.By providing detailed research of elastic waves from the theory,experiment and the field data processing,the sphere-equivalency approach of elastic wave scattering has been used to model the elastic moduli of solid containing aligned cracks.We analyze the characteristics of elastic wave propagation in different kinds of anisotropic mediums.We then develop the measurement technology of anisotropy evaluation from the borehole acoustic waves.We present some typical data processing applications.The major work of this paper consists of three parts as follows.In the first part,theoretical model has been analyzed to describe the effective elastic properties of cracked media.We first provide the most popular theoretical models and and analyses its advantage and disadvantage and applicability.In this study,we utilize a sphere-equivalency approach for elastic-wave scattering to model the anisotropic characteristics of cracked rocks.Consider an isotropic,homogeneous,elastic background matrix containing aligned ellipsoidal cracks.The resulting moduli are therefore anisotropic because of the crack alignment.The sphere-equivalency approach is a methodology that equates the far-field elastic waves scattered by the cracks to the waves scattered by a sphere whose elastic moduli are equivalent to those of the same solid containing the cracks.The merit and accuracy have been demonstrated by comparison to existing theories,and then verified using available experimental data.The new theoretical modeling result is more accurate and stable for higher crack concentrations than those of the existing Eshelby-Cheng and Hudson's models under both dry and water-saturated conditions.In the next,we have developed a technique to model the effective moduli of TI media containing cracks.We analyze the propagation characteristics for different kinds of anisotropic models.In the second part,we focus on the anisotropy evaluation method of the VTI formation from borehole acoustic measurements.First,we first describe the acoustic theory for borehole multipole-wave propagation with a VTI formation and perform a sensitivity analysis of the multipole(monopole and dipole)wave to the TI parameter.We include the tool in our analysis because it affects the wave propagation characteristics and must be properly modeled in the field data analysis.We then develop the inversion method to extract the anisotropy parameter from field data.Our analysis shows that the Stoneley wave is sensitive to the TI property mainly in an acoustically slow formation,and the sensitivity diminishes when the formation become faster.The advantage of the flexural wave over the Stoneley wave is that the former wave is sensitive to the TI property in both slow and fast formations,provided the wave measurement is made in a broad frequency-range in which the flexural-wave dispersion characteristics from low to high frequencies can be utilized.We have developed a joint inversion method for multipole acoustic data processing in the slow formation to simultaneously determine formation shear-wave transverse isotropy and vertical shear-wave velocity.By jointly combining the Stoneley and flexural wave dispersion data of different frequency band,we finally improve accuracy of the inversion.In the third part,the anisotropy evaluation method of the HTI formation from borehole acoustic measurements has been studied.First,the propagation characteritics of flexural wave in a borehole surrounded by an HTI formation have been analyzed.The phenomenon of shear wave splitting is occurred when the formation is azimuthally anisotropic.We then present a super-reverse-virtual(SRV)interferometry based on the super-virtual(SV)interferometric method.By averaging the SRV and SV results over all receiver positions in array,the S/N ratio of formation signals can be significantly enhanced.In the next,we present a inversion method to extract the azimuthal anisotropy parameter from cross-dipole array data based on elastic-wave velocity variation around borehole.This method uses the travel-times of the fast and slow shear waves,not just the diffencences of these two waves.The simualation and field processing show that this medthod is more suitable for the multi-crack-sets cases.Based on the analysis above,we try to explain the field data processing results,including formation stress,shale data processing,hydraulic fracturing evaluation,fracture analysis,and rock mechanics.As a matter of fact,our study can be used to many more applications,such as anisotropy measurement in deviated well and single-well acoustic imaging in anisotropy formation and so on.