3D NUMERICAL SIMULATION OF BOREHOLE SONIC MEASUREMENTSACQUIRED IN DIPPING, ANISOTROPIC, AND INVADED FORMATIONS

摘要

Borehole sonic measurements acquired in high-anglewells can be influenced by shoulder-bed effects,anisotropy resulting from sand-shale laminations, unbalanced(tensor) formation stresses, and fractures. Presenceof mud-filtrate invasion can further impact themeasurements, thereby complicating the interpretationof sonic logs and biasing the estimation of elasticproperties of rock formations.This paper describes a numerical simulation studyof borehole sonic measurements acquired in highanglewells. We examine effects due to shoulder beds,anisotropy, and mud-filtrate invasion on simulated sonicwaveforms. Specifically, we analyze the effects on flexuraland Stoneley wave frequency-dispersion curves, asthese are commonly used to estimate elastic propertiesof rock formations.Numerical simulations are considered for a range ofmodels for both fast and slow formations. Computationsare performed with a Cartesian three-dimensional(3D) finite-difference time-domain (FDTD) code thatmodels elastic wave propagation in a fluid-filled borehole.Resultant time domain waveforms collected acrossthe receiver array are processed to produce frequencyslownessdispersion curves.Simulations show that presence of anisotropy alters thedegree of dispersion observed in flexural and Stoneleywaves. For example, in slow formations exhibitingtransverse isotropy, the flexural wave is less dispersivethan for the case of an isotropic formation, wherechanges in phase slowness, relative to the slownessobserved at the low frequency cutoff, decrease by asmuch as 30% at higher frequencies. Stoneley wavedispersion, on the other hand, increases in anisotropicformations than in isotropic formations, where changesin phase slowness, relative to the slowness observed atlow frequencies (tube wave slowness), increase by morethan a factor of 2.5 at higher frequencies.We also found that the impact of invasion on flexuraland Stoneley dispersions is altered by presenceof anisotropy. In the case of slow formations exhibitingtransverse isotropy, separation between dispersioncurves for cases with and without presence of invasionincrease by as much as 33% for the flexural wave andby as much as a factor of 1.4 for the Stoneley wavewith respect to cases in isotropic formations.Lastly, presence of a shoulder bed intersecting the sonictool at high dip angles can significantly alter flexuraldispersion at low frequencies, making it difficult toidentify the low frequency asymptote corresponding toformation shear wave velocity. For cases of the shoulderbed dipping at 80?, ambiguity in the flexural cutofffrequency may lead to shear wave velocity errors of8-10%.