Empirical Formula for Dynamic Biot Coefficient of Sandstone Samples from South-West of Poland

In this research, two empirical correlations have been introduced to calculate the dynamic Biot coefficients of low-porosity and high-porosity sandstone samples from two open pit mines located in South-West Poland. The experiments were conducted using an acoustic velocity measurement apparatus. Under the undrained condition, firstly, the confining pressure was increased in increments of 200 psi, and the values of pore pressure and dynamic elastic modulus were recorded. This experiment was continued until the Skempton coefficient remained in the range of 0.98–1. Secondly, an experiment on the same sample was conducted under drained conditions, and the corresponding dynamic elastic moduli were calculated. Then, using the calculated dynamic elastic moduli, the dynamic Biot coefficient was determined for each sample under different confining pressure. Finally, two empirical correlations were formulated for each sandstone category. The results demonstrate that, as the confining pressure increases, the Biot coefficient decreases from 0.79 to 0.50 and from 0.84 to 0.45 for low-porosity and high-porosity samples, respectively. Furthermore, as the porosity increases, the sandstone behavior increasingly approaches that of soil. The empirical correlations can be used for sandstone formations with the same porosity in projects where there is not a measurement method for the Biot coefficient.

Direct measurement of the unjacketed pore modulus of porous solids

Pressure decline caused by the extraction of oil from deep sedimentary layers depends on the pore modulus K pp , a poroelastic parameter that characterizes the effect of pressure change on pore volume under constant mean stress. Measurement of K pp is difficult, however, as it requires calibration to account for fluid compressibility and compliance of the testing system. Nevertheless, knowing the easily measurable drained pore modulus K p and adopting an assumption on the unjacketed pore modulus K s ″, it is possible to determine K pp because these pore moduli are related. Previous work on indirectly estimating K s ″ claimed that K s ″ is strongly dependent on Terzaghi effective pressure P′ and therefore not a constant; also, K s ″ might be different from K s , the solid bulk modulus of the major mineral constituent. We overcome the limitations of the indirect approach by directly measuring K s ″. The experiments reveal that K s ″ is indeed a constant and that for an ideal porous rock, the assumption of K s ′ ′ = K s holds. Furthermore, a constant K s ″ implies that K p and K pp are functions of Terzaghi effective pressure only. These results provide a framework to accurately determine the Skempton coefficient B .