Experimental Determination of the Anisotropic Elastic Properties of Shales
The ultrasonic anisotropic elastic properties of shales were measured as a function of effective pressure. Due to the low permeability of shales special equipment and techniques were required to control the over burden pressure and the sample pore pressure. An initial study looked at a preserved shale specimen of Jurassic age. Here measurements of compressional and shear wave velocities were taken on a set of three plugs cut from the shale and oriented at three angles (0, 90 and 45 degrees) with respect to the visual axis of symmetry. These measurements were taken at pressures up to 110 MPa and with the pore pressure drained to atmosphere. Next, an inversion procedure was created to reconstruct elastic stiffnessessusing the measured velocities. This inversion procedure involved taking an overdetermined set of measurements (minimum of 9 measurements for 3 sample plugs)and then minimizing a cost function based on the mis-fit between the predicted phase slownes surface and the laboratory measured slownesses. The final rms error for the reconstruction using the three samples was low, less than 3 μ/m. With a different block of the same shale, an additional experiment used a series of five plugs cut at five different angles relative to the axis of symmetry. The objective of this experiment was to make a additional test on the estimation of the elastic stiffnesses, and in particular for C13, using a greatly overdetermined set data. The five samples gave a set of 15 measurements with which to estimate the 5 elastic parameters. The resultant reconstruction of elastic constants gave a low rms error of approximately 4 μs/m. In addition, the elastic stiffnesses for the separate blocks of shale were in dose agreement, suggesting that data sets collected on this shale may be representative.
The reconstructed elastic stiffnesses for the experiment using the three samples were then analyzed in terms of their anisotropy and other properties as a function of effective stress. Up to 26 percent compressional wave anisotropy (Thompson’sparameter, ε) and up to 48 percent shear wave anisotropy (Thompson’s parameter,γ) was observed and it was found that both εγ and decreased as a function of increasing effective stress. In addition the anellipticity (deviation of the slowness surfaces from ellipses) was found to be positive and also decreased as a function of increasing effective stress. This decrease in anisotropy and anellipticity with increasing effective stress was accompanied by a corresponding decrease in porosity of the sample, from 10 1/2 to 8 1/2 percent. The decrease in overall anisotropy of the shales with increasing effective stress was seen to be consistent with theoretical modeling of shale properties where the shale anisotropy and anellipticity were predicted to decrease as a function of decreasing fluid filled porosity.