Lasse Renlie

Radial profiling of the three formation shear moduli and its application to well completions

Near-wellbore alteration in shear stiffnesses in the three orthogonal planes can be described in terms of radial variations of the three shear moduli or slownesses. The three shear moduli are different in formations exhibiting orthorhombic or lower degree of symmetry, as is the case in deviated wellbores in triaxially stressed formations. These shear moduli are affected by factors such as overbalanced drilling, borehole stress concentrations, shale swelling, near-wellbore mechanical damage, and supercharging of permeable formations. The two vertical shear moduli C44 and C55 in an anisotropic formation with a vertical x3 -axis are obtained from crossed-dipole sonic data, whereas the horizontal shear modulus C66 is estimated from borehole Stoneley data. The effective shear modulus C66 is smaller than the vertical shear moduli C44 or C55 in a poroelastic formation exhibiting high horizontal fluid mobility. Consequently, analyses of radial profiling of the three shear moduli in a reasonably uniform lithology ...

High‐order, finite‐difference modeling of multipole logging in formations with anisotropic attenuation and elasticity

A realistic description of the formation seen by an acoustic logging tool includes intrinsic attenuation, anisotropy, and spatial variations of the formation properties. These features are included in finite-difference (FD) modeling of acoustic full waveform multipole logging. Intrinsic attenuation is included using a phenomenological model that allows for many physical causes of attenuation, including viscous fluid flow losses, to be modeled. Furthermore, the attenuation, the corresponding velocity dispersion, and the elasticity can have any type of axisymmetric anisotropy. To increase computational speed and numerical precision, high-order FD operators that fully exploit vector processing architecture are used. The problem of using these operators near the symmetry axis in cylindrical coordinates is solved using symmetry arguments. Excellent results are obtained when comparing the calculations with the discrete wavenumber method. When correctly implemented, the FD model has the same numerical precision as the discrete wavenumber method but allows more general formations to be analyzed. Incorrect staggering of the high-order FD scheme gives artifacts equivalent to the inclusion of a thin layer between the fluid and the formation.

Acoustic wave propagation in a fluid-filled borehole surrounded by a formation with stress-relief-induced anisotropy

The stress relief associated with the drilling of a borehole may lead to an anisotropic formation in the vicinity of the borehole, where the properties in the radial direction differ from those in the axial and tangential directions. Thus, axial and radial compressional acoustic velocities are different, and similarly, the velocity of an axial shear‐wave depends on whether the polarization is radial or tangential. A model was developed to describe acoustic wave propagation in a borehole surrounded by a formation with stress‐relief‐induced radial transverse isotropy (RTI). Acoustic full waveforms due to a monopole source are computed using the real‐axis integration method, and dispersion relations are found by tracing poles in the kz plane. An analytic expression for the low‐frequency Stoneley wave is developed. The numerical results confirm the expectations that the compressional refraction is mainly given by the axial compressional velocity, while the shear refraction arrival is due to the shear wave wit...

Multipole logging in a formation with stress-relief-induced anisotropy

The stress relief associated with the drilling of a borehole may induce a mechanically damaged zone with radial transverse isotropy (RTI), where the properties in the radial direction differ from those in the axial and tangential directions. The effect of such a zone on multipole acoustic full‐waveform logging is investigated using a numerical model based on the frequency‐axial‐wavenumber method. Calculations of the spectral behavior show that the fundamental mode associated with the multipole source behaves the same way in an RTI zone as it does in a damaged zone with isotropic properties. In a slow virgin formation, calculations of full waveforms show that the presence of a damaged zone with RTI is more difficult to detect than a damaged zone with isotropic elasticity because the refracted P‐wave encounters an isotropic zone but not an RTI zone. The results indicate that a damaged zone with RTI, which is a precursor to destructive events such as borehole instability and sand production, can be detected ...