Colin M. Sayers1 and Lennert D. den Boer2
The layered structure of clay minerals produces large elastic anisotropy due to the presence of strong covalent bonds within layers and weaker electrostatic bonds in between. Technical difficulties associated with small grain size preclude experimental measurement of single-crystal elastic moduli. However, theoretical calculations of the complete elastic tensors of several clay minerals have been reported, using either first-principle calculations based on density functional theory or molecular dynamics. Because of the layered microstructure, the elastic stiffness tensor obtained from such calculations can be approximated to good accuracy as a transversely isotropic (TI) medium. The TI-equivalent elastic moduli of clay minerals indicate that Thomsen’s anisotropy parametersand are large and positive, whereas is small or negative. A least-squares inversion for the elastic properties of a best-fitting equivalent TI medium consisting of two isotropic layers to the elastic properties of clay minerals indicates that the shear modulus of the stiffest layer is considerably larger than the softest layer, consistent with the expected high compliance of the interlayer region in clay minerals. It is anticipated that the elastic anisotropy parameters derived from the best-fitting TI approximation to the elastic stiffness tensor of clay minerals will find applications in rock physics for seismic imaging, amplitude variation with offset analysis, and geomechanics.
Measurements of elastic and electrical properties of an unconventional organic shale under differential loading
1Colorado School of Mines, Department of Geophysics, Golden, Colorado, USA. E-mail: firstname.lastname@example.org; email@example.com.
2Colorado School of Mines, Department of Geophysics, Golden, Colorado, USA and Université Savoie Mont Blanc, ISTerre, CNRS, UMR CNRS, Le Bourget du Lac, France. E-mail: firstname.lastname@example.org
3Colorado School of Mines, Department of Geophysics, and Department of Petroleum Engineering, Golden, Colorado, USA.
4University of Texas at Austin, Department of Petroleum and Geosystems Engineering, Austin, Texas, USA. E-mail: email@example.com.
We have developed an experimental approach to simultaneously measure the stress dependence of ultrasonic wave velocities at 1 MHz, and therefore the components of the undrained elastic stiffness tensor, as well as the components of the complex conductivity tensor in the frequency range from 100 mHz to 10 Hz. We performed the experiments on a cylindrical core sample from the Haynesville Formation (porosity of approximately 0.08, bound water excluded, and clay content, mostly illite, approximately 30–40 wt%). We performed experiments under controlled confining and pore fluid pressures, achieving differential pressure states representative of autochthonous reservoir conditions. Directional measurements were made using independent acquisition arrays (piezoelectric crystals and nonpolarizing electrodes) distributed azimuthally on the core sample external surface, the bedding plane being along the axis of the cylindrical core sample. Ultrasonic waveforms were recorded on a high-resolution oscilloscope, and complex impedance spectra were recorded with a four-electrode acquisition system using an impedance meter with precision of 0.1 mrad. Experiments were repeated under drained and undrained conditions, over loading and unloading sequences for fully water-saturated conditions. Measurements show strong stress dependence on ultrasonic and complex conductivity measurements, which can be ascribed to the opening and closing of cracks within the samples. The data were used to estimate the anisotropic electrical and elastic effective pressure coefficients of the core sample, resulting in effective stress coefficients smaller than one for both elastic and electrical properties. These effective stress coefficients were also smaller for the electrical and acoustic properties once the cracks have closed. The anisotropy ratio for the components of the complex conductivity tensor was on the order of 30, whereas it was only 2 for the compressional components of the stiffness tensor ().
The effect of systematic diagenetic changes on the mechanical behavior of a quartz-cemented sandstone
Jennie E. Cook, Laurel B. Goodwin, David F. Boutt, and Harold J. Tobin - A key goal of petrophysical studies of sandstones is to relate common field measurements, particularly seismic or sonic velocities, to parameters defining the rock’s mechanical and hydrologic characteristics. These include elastic and inelastic mechanical properties, porosity, and permeability. We explored relationships among these properties in variably quartz-cemented, mature arenites of the St. Peter Sandstone with porosities ranging from 9% to 25%. In a previous paper, we described microstructural changes accompanying progressive quartz cementation and related porosity and permeability reduction in this sample suite. Here, we report ultrasonic velocities ultrasonic velocities, dynamic and static elastic properties, confined compressive strength, and tensile strength. Analyses of these data demonstrated that factors controlling permeability also fundamentally determined the elastic and inelastic mechanical properties. We found that the number of grain contacts, or bonds, per number of grains viewed in the thin section (bond-to-grain ratio [BGR]) was a key predictive parameter of the mechanical and hydrologic properties. Although the contact length and number of contacts correlated well with the mechanical behavior, statistical analyses showed that BGR was a better predictor of strength, elastic stiffness, and fluid transport properties than was the contact length. The BGR provided a measure of the pore throat occlusion that reduced permeability and the connectivity of the grain framework that stiffened and strengthened the rock. Because porosity and BGR were typically well correlated, porosity was a more quickly and easily measured proxy for BGR in this case. However, our analysis showed that it was the microstructural changes associated with porosity loss rather than porosity loss per se that largely controlled the properties of interest. Thus, consideration of BGR as well as the relative strengths of grains and bond type (cement, pressure solution) for different compositions of sandstone and cement may constructively form the basis for comparative studies of other more complex sandstones.
Read More: http://library.seg.org/doi/abs/10.1190/geo2014-0026.1