Effect of Pressure on Compression, Shear and Young’s Moduli

The rocks response as perfectly elastic materials in case of rapidly changing stresses. With the assumption of the Hooke body, the elastic moduli describe how rocks resist different deformations. Present investigations covered the examination of pressure dependence of compressional, shear and Young’s moduli. As they can be calculated from the acoustic wave velocities (longitudinal and transverse) it is important to know accurately the velocity-stress function. Therefore the authors developed a petrophysical model, which gives the physical connection between the acoustic velocities and stresses. After estimating the model parameters by joint inversion, where the rock physical parameter is the common parameter, the velocities can be calculated at any arbitrary stresses and the pressure dependent elastic moduli can be derived. To prove the applicability of this method, we measured P and S wave velocities on sandstone samples with an automatic acoustic test system under uniaxial load. This paper includes one sample from these measurements together with literature data of a Berea sandstone sample. The results show that the misfits between measured and calculated data are small, the model can be applied well in practice.