New petrophysical models verified on laboratory data measured by an automatic acoustic test system

Understanding the relationship between pressure and rock physical parameters, such as acoustic velocities, absorption coefficients, elastic moduli, porosity is essential for exploring and exploiting of natural reserves. In this study petrophysical models are introduced which describe the relationship between acoustic longitudinal (P), transverse (S) wave velocities as well as quality factors and pressure. The governing equations of the models are based on the idea that the pore volume of a rock is decreasing with increasing pressure. To prove the applicability of the models, we measured P and S wave velocities in laboratory on sandstone samples by an automatic acoustic test system under uniaxial load. The loading of the samples were carried out by the Freely Programmable Interface module of the software DION 7. The velocities were measured automatically by the software GMuG/GL Test Systems PCUSpro. We applied 256-fold stacking to increase the signal/noise ratio. Acoustic velocities were measured by using the pulse transmission technique. By applying the programmed algorithm and the acoustic software the measurements have become completely automatic. On the other hand quality factor data set - published in literature - as a function of pressure was inverted too. After estimating the model parameters by joint inversion method, the velocities and quality factors can be calculated at any arbitrary stresses and the pressure dependent elastic moduli as well as loss angles can be derived. The quality checked joint inversion results showed that the misfits between measured and calculated data are small, the suggested petrophysical models can be applied well in practice.