Borehole flexural waves in formations with radially varying properties

Abstract

Elastic wave propagation in a fluid-filled borehole is affected by near-wellbore alteration of formation properties. Near-wellbore alteration can be caused by several sources, such as overbalance drilling, borehole stress concentrations, shale swelling, near- wellbore mechanical damage and supercharging of permeable formations. Optimal completions of a well for production require both identification and estimation of the radial extent of alteration in reservoir intervals. Measured borehole flexural dispersions in the presence of radial gradients in formation properties can be inverted to estimate the radial extent of mechanical alteration. However, the presence of a tool structure that carries the acoustic transmitters and hydrophone receivers also introduces certain amount of bias on the measured borehole flexural dispersions. This paper describes the Backus-Gilbert inversion of synthetic borehole flexural data for radial variation in formation shear slowness (slowness is inverse of velocity). The inversion algorithm accounts for the tool bias on the measured data by introducing an equivalent structure of a heavy-fluid column placed concentrically with the borehole axis. This simple structure enables computation of the eigensolution for a reference homogeneous and isotropic formation that are used for calculating the data kernel in the perturbation integral equation. The solution of this integral equation yields the radial variation in the formation shear modulus in terms of fractional differences in the measured and reference dispersion at various wavenumbers. Results are presented for both radially increasing and decreasing shear slownesses away from the borehole.