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Formation Property Estimation from Guided Wavesby Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on November 25, 1986 in partial fulfillment of the requirements for the degree of Doctor of Philosophy ABSTRACT
A detailed sensitivity analysis of the effects of elastic parameter perturbations
on the velocity and amplitude of borehole guided waves is carried out for the
simple open borehole geometry as well as the radially layered geometry which occurs
when an altered zone is present in the formation or casing is introduced into
the borehole. The results of this analysis indicate that the Stoneley and pseudo-Rayleigh
waves are sensitive to variations in the formation shear wave velocity and shear
wave attenuation factor. The Stoneley wave is the most sensitive to these properties
at frequencies near the cutoff frequency. Because the Stoneley wave is controlled
by the properties of the layers immediately adjacent to the borehole wall, the
presence of an altered zone in the formation can have a significant effect on
the Stoneley wave behavior. The presence of casing also has a large effect. The
depth of investigation of the pseudo-Rayleigh wave increases with decreasing frequency,
therefore, the presence of an altered zone or casing effects the velocity and
attenuation of this wave at intermediate frequencies. Both waves are very sensitive
to the borehole fluid properties and variation in borehole radius. In order
to investigate the effect of borehole fluid viscosity on the guided wave attenuation
and dispersion, the wave propagation problem in a borehole containing a viscoelastic
fluid surrounded by an infinite elastic formation is solved using boundary layer
theory. The results indicate that the viscous drag losses are a small component
of the overall guided wave attenuation for the frequencies of interest in full
waveform acoustic logging (2-15kHz) and for reasonable viscosity values (1-1000
cP). These losses, however, can be significant at low frequencies. The results
of this study indicate friction between grains in fluid suspension may be the
dominant attenuation mechanism in the drilling fluids present in boreholes. A
linear least squares inversion, based on analytic coefficient expressions, is
developed to estimate the fluid and formation shear wave Q values from spectral
ratio measurements of the Stoneley and pseudo-Rayleigh waves in open boreholes.
The method provides excellent results when applied to synthetic data. Real data
applications provide useful results, but noise reduces the resolution and increases
the variance of the estimates. Permeability related losses and transmission losses
(if interfaces are present) can have large effects on the estimated values. A
similar procedure is developed for cased hole geometries. In this situation, the
guided wave measurements are used to provide estimates of the fluid, formation
shear wave, and cement shear wave Q values. Application of the method to synthetic
data indicates that the formation shear Q estimate is extremely sensitive to the
pseudo-Rayleigh wave data quality very close to the cutoff frequency. Stoneley
wave phase velocity and attenuation measurements show excellent correlation with
core measured permeability values in many situations. The phase velocity decreases
and the attenuation increases with increasing permeability. Calculations are carried
out using the Rosenbaum formulation of wave propagation in a borehole surrounded
by a Biot porous solid. The formulation is modified to include intrinsic attenuation
in the borehole fluid and formation. Forward modeling results indicate that the
model can explain the attenuation variations seen in real data, but cannot adequately
explain the phase velocity variations. The presence and properties of a mudcake
layer along the borehole wall may play a key role in the Stoneley wave behavior.
A linearized least squares inversion is developed based on the Biot-Rosenbaum
model which uses measured Stoneley wave spectral ratios as input. The resulting
permeability estimates are in general agreement with the measured values obtained
from two boreholes. The Stoneley wave phase velocity measurements provide a very
good measure of relative permeability variations when corrected for all elastic
property changes. Return to Theses Return to ERL Home Updated: June,1999
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