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

Abstract

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.