Elastic properties of sands, Part 2: Implementation of contact‐based model to determine the elasticity of the grains from ultrasonic measurements

Abstract

ABSTRACTThe prediction of effective elastic properties of a granular medium using ultrasonic data based on contact models has been studied widely in both laboratory experiments and numerical simulations. In contrast, a calculation of the elastic properties of the constituent grains using similar data by inverting the equations from those models is a rather new concept. To do so, we have developed a controlled experiment technique that includes a uniaxial compaction test and measures ultrasonic velocities of four unconsolidated quartz sand samples with different sorting and grain shapes. We observe that both P‐ and S‐wave velocities are significantly influenced by the microstructure or internal arrangement of the grains. Well sorted and more spherical and rounded samples show higher velocities than the poorly sorted and less spherical and rounded samples. A microstructural parameter – namely coordination number – we have calculated from high resolution micro computed tomography images provides a good match between the model and dynamic effective bulk moduli of the sand pack. Combining this coordination number with a frictional parameter calculated from the measured velocity ratios has been very effective to fit the model with the dynamic effective shear moduli. Using these two key parameters along with the experiment results in the contact model we have been able to obtain the elastic parameters of the quartz sand grains in the sample. Elastic parameters obtained thus are very close to the actual values of the quartz grains found in the literature. This technique can be useful in hard rock mineral exploration where missing core samples or an absence of well logs can be replaced by laboratory measurements of powders to find the elasticity or velocities of the rocks. Moreover, the elastic properties of the solid phase calculated using this technique can be used as input parameters for the fluid substitution and rock physics characterization of unconsolidated reservoir sands.