A New Experimental Design to Measure Second- and Third-Order Anisotropic Rock-Stiffness Coefficients Using a Single-Rock Sample

Abstract

We developed a new experimental setup for measuring and modelling stress-induced anisotropy and nonlinearity in cylindrical rock samples. Multidirectional ultrasonic velocity measurements were conducted under laboratory conditions and during triaxial-stress testing to capture dynamic rock properties. This is done by placing endcap transducers (ECTs) and small-piezoelectric transducers (SPT) distributed axially and azimuthally along the sample. To validate the method, we used aluminium and phenolic samples under ambient conditions. Measurements were acquired from ECT–ECT, SPT–SPT and ECT–SPT combinations. The SPT–SPT combination increases the number of azimuthal sensors to eight at a single level. The ECT–SPT is evaluated as a new possible transducer combination to evaluate waveform propagation along the sample axis. After validation, triaxial-stress testing was performed on Berea Sandstone and Mancos Shale core samples, using only ECT–ECT and SPT–SPT measurements. Each core sample was subject to isotropic and triaxial compression stress paths. During the triaxial-stress testing on Berea Sandstone and Mancos Shale, we measured P- and S-wave velocities along the sample axis ($v_{P_{\mathrm{ph}}}^{90}$, $v_{S_{\mathrm{ph}}}^0$ and $v_{S_{\mathrm{ph}}}^{90}$) and Tsvankin's anisotropy parameters ${\epsilon }^{\left(1\right)}$, ${\epsilon }^{\left(2\right)}$ and ${\delta }^{\left(3\right)}$. We analyse stress-induced changes in stiffness, anisotropy and elastic nonlinearity in both parallel and perpendicular directions to the sample symmetry axis to estimate second- and third-order elastic stiffness coefficients. We observe, using a single Mancos Shale sample, that an increase of hydrostatic stress from 6.8 to 34.5 MPa decreases ${\epsilon }^{\left(2\right)}$ from 0.08 to 0.05. During the triaxial-compression stress path, an increasing axial-loading stress was applied parallel to the $C_{11}$ direction. For an axial stress increase from 24 to 48 MPa, we observe that ${\epsilon }^{\left(2\right)}$ increases from 0.12 and 0.09 to 0.16 and 0.2 for Berea Sandstone and Mancos Shale, respectively. Results from our work indicate that both ECT and SPT measurements are critical to improve the quantification of stress-induced dynamic properties of rocks.