Determining the transverse isotropic rock’s static elastic moduli with cylindrical plugs: shortfalls, challenges and expected outcomes

Cylindrical shaped plugs can be tested using a Hoek-Cell like apparatus that allows for efficient and inexpensive measurements of a rock’s static elastic properties. However, when it comes to Transverse Isotropic material, this approach has a natural limitation due to the isotropic radial stresses; particular attention to the boundary conditions and the proper design of pressurization steps is warranted. Typical attempts to constrain the complete set of compliances ( S), using multiple plugs of different orientations, are impeded by the heterogeneity and pressure-dependent elasticities inherent to sedimentary rocks. Through stepwise pressure increases, we can constrain four normal compliances S 11, S 12, S 13, S 33 , describing two Young’s moduli and three Poison’s ratios using a single horizontal plug drilled parallel to the rock’s isotropic plane, contrary to the common assumption that at both horizontal and vertical plugs are needed. The measurement of the shear modulus S 44 needs to be obtained using a plug that is drilled oblique to the isotropic plane; replicating the in-situ stress environment is not possible using this approach. Lastly, the specimen’s anisotropic plane’s geometry is elliptical under isotropic radial stress; this causes a discrepancy between the strain gauge’s contraction and the actual strain. We propose an iterative inversion approach to account for this issue and calculate the exact strains useful for inferring S ij from measurements reported by strain gauges. The example included in this writing shows that without correction, inferred values of S ij may suffer errors of 20%.

Determining elastic properties of sedimentary strata in terms of limestone samples by laser ultrasonics

Geological engineering often uses geomechanical modeling aimed to enhance efficiency of mining or performance of structures. One of the input parameters for such models are the static elastic moduli of rocks. This article presents the studies into the physical and mechanical properties of rocks-limestone of non-metamorphic diagenesis. The precision measurements of Pand S-waves are carried out to an accuracy of 0.2% by laser ultrasonics. The static moduli of elasticity and the deformation characteristics of rocks are determined in the uniaxial compression tests by the standards of GOST 21153.2-84 and GOST 28985-91, respectively. The correlation dependence is found between the static and dynamic elasticity moduli in limestone samples. The found correlation allows drawing the conclusion that the static modulus of elasticity can be estimated in non-destructive tests, which largely simplifies preliminary diagnostics of samples in case of limited number of test core.

Comparison of elastic moduli from seismic diving-wave and ice-core microstructure analysis in Antarctic polar firn

ABSTRACTWe compared elastic moduli in polar firn derived from diving wave refraction seismic velocity analysis, firn-core density measurements and microstructure modelling based on firn-core data. The seismic data were obtained with a small electrodynamic vibrator source near Kohnen Station, East Antarctica. The analysis of diving waves resulted in velocity–depth profiles for different wave types (P-, SH- and SV-waves). Dynamic elastic moduli of firn were derived by combining P- and S-wave velocities and densities obtained from firn-core measurements. The structural finite-element method (FEM) was used to calculate the components of the elastic tensor from firn microstructure derived from X-ray tomography of firn-core samples at depths of 10, 42, 71 and 99 m, providing static elastic moduli. Shear and bulk moduli range from 0.39 to 2.42 GPa and 0.68 to 2.42 GPa, respectively. The elastic moduli from seismic observations and the structural FEM agree within 8.5% for the deepest achieved values at a depth of 71 m, and are within the uncertainty range. Our observations demonstrate that the elastic moduli of the firn can be consistently obtained from two independent methods which are based on dynamic (seismic) and static (tomography and FEM) observations, respectively, for deeper layers in the firn below ~10 m depth.

A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations

We obtained the complete set of dynamic elastic stiffnesses for a suite of “shales” representative of unconventional reservoirs from simultaneously measured P- and S-wave speeds on single prisms specially machined from cores. Static linear compressibilities were concurrently obtained using strain gauges attached to the prism. Regardless of being from static or dynamic measurements, the pressure sensitivity varies strongly with the direction of measurement. Furthermore, the static and dynamic linear compressibilities measured parallel to the bedding are nearly the same whereas those perpendicular to the bedding can differ by as much as 100%. Compliant cracklike porosity, seen in scanning electron microscope images, controls the elastic properties measured perpendicular to the rock’s bedding plane and results in highly nonlinear pressure sensitivity. In contrast, those properties measured parallel to the bedding are nearly insensitive to stress. This anisotropy to the pressure dependency of the strains and moduli further complicates the study of the overall anisotropy of such rocks. This horizontal stress insensitivity has implications for the use of advanced sonic logging techniques for stress direction indication. Finally, we tested the validity of the practice of estimating the fracture pressure gradient (i.e., horizontal stress) using our observed elastic engineering moduli and found that ignoring anisotropy would lead to underestimates of the minimum stress by as much as 90%. Although one could ostensibly obtain better values or the minimum stress if the rock anisotropy is included, we would hope that these results will instead discourage this method of estimating horizontal stress in favor of more reliable techniques.