Estimation of stress-dependent anisotropy from P-wave measurements on a spherical sample

Abstract

Our aim is to understand the stress-dependent seismic anisotropy of the overburden shale in an oil field in the North West Shelf of Western Australia. We analyze data from measurements of ultrasonic P-wave velocities in 132 directions for confining pressures of 0.1-400 MPa on a spherical shale sample. First, we find the orientation of the symmetry axis, assuming that the sample is transversely isotropic, and then transform the ray velocities to the symmetry axis coordinates. We use two parameterizations of the phase velocity; one, in terms of the Thomsen anisotropy parameters a, b, e, d as the main approach, and the other in terms of a, b, g, d. We invert the ray velocities to estimate the anisotropy parameters a, e, d, and g using a very fast simulated reannealing algorithm. Both approaches result in the same estimation for the anisotropy parameters but with different uncertainties. The main approach is robust but produces higher uncertainties, in particular for g, whereas the alternative approach is unstable but gives lower uncertainties. These approaches are used to find the anisotropy parameters for the different confining pressures. The dependency of P-wave velocity, a, on pressure has exponential and linear components, which can be contributed to the compliant and stiff porosities. The exponential dependence at lower pressures up to 100 MPa corresponds to the closure of compliant pores and microcracks, whereas the linear dependence at higher pressures corresponds to contraction of the stiff pores. The anisotropy parameters e and d are quite large at lower pressures but decrease exponentially with pressure. For lower pressures up to 10 MPa, d always is larger than e; this trend is reversed for higher pressures. Despite the hydrostatic pressure, the symmetry axis orientation changes noticeably, in particular at lower pressures.

Combined Effects of Pressure and Water Saturation on the Seismic Anisotropy in Artificial Porous Sandstone With Aligned Fractures

“…To minimize such effect arising from the multicore measurement, experimental methods have been developed to measure five independent velocities on a single plug under pressure to fully characterize the seismic anisotropy of a transversely isotropic (TI) rock. The single plug can be octagonal or even spherical samples (e.g., Ding et al, ; Han, ; Nadri et al, ; Tillotson et al, ), but most commonly is a cylindrical core drilled parallel to the anisotropy plane (Dewhurst & Siggins, ; Sarout et al, ; Wang, ). While all the above experimental methods can be employed to measure the variation of seismic anisotropy with water saturation, the single cylindrical core technique is considered to be the most feasible method to determine the saturation effects on the pressure‐dependent seismic anisotropy.…”

Estimation of the anisotropy parameters of transversely isotropic shales with a tilted symmetry axis

“…A comprehensive description of the experimental set‐up is given by Pros et al (1998). Table 2 shows a comparison between the estimates obtained with the current approach (‘coupled inversion’) and the previous approach described by Nadri et al 2011a (‘uncoupled inversion’). The two estimates are very similar.…”

“…In a recent approach, Nadri et al (2011a) and Bóna et al (2012) used ultrasonic P ‐wave velocity data from a spherical shale sample to determine its elastic anisotropy parameters assuming transverse isotropy. However, to compute the phase velocities from the measured ray velocities, they first determined the orientation of the symmetry axis and defined the principal reference coordinate system aligned with the elastic symmetry axes.…”

“…Ultrasonic P ‐wave velocity data sets from two different shales are then described: a spherical sample from the North West Shelf in Western Australia subjected to 40 MPa confining pressure and a cylindrical sample from the Opalinus Clay formation in Switzerland subjected to 45 MPa confining pressure and 5 MPa pore pressure. The data and associated interpretation in terms of anisotropy from the spherical sample (already published by Nadri et al 2011a and Bóna et al 2012) are used for the validation of the new method. This method is then applied to the case of the cylindrical shale sample.…”

Laboratory measurement of elastic anisotropy on spherical rock samples by longitudinal and transverse sounding under confining pressure

“…The study of the velocity anisotropy of V P on spherical samples provides more complete information of the velocities in any direction both under atmospheric and high hydrostatic pressures [21][22][23][24][25][26][27][28].…”