ABSTRACT

Sonic logging through casing is of increasing interest in the oil and gas industry. However, 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 cased hole. The cement annulus behind the casing together with drilling-induced near-wellbore alteration causes radial heterogeneity in the propagating medium. It is, therefore, necessary to study the influence of such heterogeneities on the borehole waves and estimate the radial extent of near-wellbore alteration in terms of radial variation of velocities away from the casing. Borehole dispersions for a radially varying formation can be obtained from a root finding mode-search routine for a multilayer cylindrical structure. In addition, a modified perturbation model based on Hamilton''s principle can also be used to predict changes in the borehole Stoneley and flexural dispersions caused by the presence of radially varying formation parameters. Unlike a classical perturbation model that uses a radially homogeneous formation as the reference state, we introduce a two-layer formation model for the reference state that is more efficient to handle a variety of formation heterogeneities. 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 surface. Numerical results using synthetic examples are presented to demonstrate the validity of this radial profiling methodology.

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