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3D NUMERICAL SIMULATION OF BOREHOLE SONIC MEASUREMENTS ACQUI

Borehole sonic measurements acquired in high-angle wells can be influenced by shoulder-bed effects, anisotropy resulting from sand-shale laminations, unbal- anced (tensor) formation stresses, and fractures. Pres- ence of mud-filtrate invasion can further impact the measurements, thereby complicating the interpretation of sonic logs and biasing the estimation of elastic properties of rock formations.
This paper describes a numerical simulation study of borehole sonic measurements acquired in high- angle wells. We examine effects due to shoulder beds, anisotropy, and mud-filtrate invasion on simulated sonic waveforms. Specifically, we analyze the effects on flex- ural and Stoneley wave frequency-dispersion curves, as these are commonly used to estimate elastic properties of rock formations.
Numerical simulations are considered for a range of models for both fast and slow formations. Computa- tions are performed with a Cartesian three-dimensional (3D) finite-difference time-domain (FDTD) code that models elastic wave propagation in a fluid-filled bore- hole. Resultant time domain waveforms collected across the receiver array are processed to produce frequency- slowness dispersion curves.
Simulations show that presence of anisotropy alters the degree of dispersion observed in flexural and Stone- ley waves. For example, in slow formations exhibiting transverse isotropy, the flexural wave is less dispersive than for the case of an isotropic formation, where changes in phase slowness, relative to the slowness observed at the low frequency cutoff, decrease by as much as 30% at higher frequencies. Stoneley wave dispersion, on the other hand, increases in anisotropic formations than in isotropic formations, where changes in phase slowness, relative to the slowness observed at low frequencies (tube wave slowness), increase by more than a factor of 2.5 at higher frequencies. We also found that the impact of invasion on flex- ural and Stoneley dispersions is altered by presence of anisotropy. In the case of slow formations exhibit- ing transverse isotropy, separation between dispersion curves for cases with and without presence of invasion increase by as much as 33% for the flexural wave and by as much as a factor of 1.4 for the Stoneley wave with respect to cases in isotropic formations.
Lastly, presence of a shoulder bed intersecting the sonic tool at high dip angles can significantly alter flexural dispersion at low frequencies, making it difficult to identify the low frequency asymptote corresponding to formation shear wave velocity. For cases of the shoulder bed dipping at 80?, ambiguity in the flexural cutoff frequency may lead to shear wave velocity errors of 8–10%.
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