Simultaneous experimental study of dynamic and static Young’s moduli in sandstones

The dynamic and static Young’s moduli of a number of reservoir sandstones were measured using ultrasonic P- and S-waves velocities in a standard uniaxial set-up. We developed and modified an experimental method to simultaneously measure the stress–strain and stress–velocity (P- and S-waves) while the samples are subjected to stress. The static and dynamic Young’s modulus and Poisson’s ratio were calculated simultaneously within the proportional limit of the stress–strain graph. For the reservoir sandstone samples with porosity ranging from 8% to 24% the dynamic Young’s modulus ranged within 4–30 GPa while the static Young’s modulus recorded within 4–17 GPa at the same time. The study determines that the dynamic elastic moduli in an isotropic material is strongly correlated to static moduli when the dynamic moduli is obtained from a direct measurement. This experimental study demonstrates the importance of registering both P- and S-wave velocities independently in order to have accurate dynamic moduli. Using conventional relations, such as Christensen’s equation, to estimate S-wave velocity from its measured P-wave introduces large errors for porous material (such as sandstones) leading to inaccurate estimation of dynamic Young’s moduli. We also examined the validity of existing equations in the literature to predict static Young’s modulus from its recorded P- and S-wave velocities. The predicted values are within the acceptable range, which adds to the validity of conducting accurate dynamic measurements for sandstones subjected to uniaxial stress.