Earth Resources Laboratory :: Abstracts

Formation Property Estimation from Guided Waves

Daniel R. Burns

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.