Effect of the fractal distribution of the radius of CO₂ patches on the ultrasonic velocity and attenuation of tight rocks

Carbon dioxide (CO 2 ) injection is currently being carried out to improve hydrocarbon recovery and reduce carbon emissions. In this study, we measure the ultrasonic velocity and attenuation during supercritical CO 2 injection into three oil-saturated tight rock samples (one sandstone and two carbonates). The experiments indicate that P-wave velocity is very sensitive to the pore-fluid substitutions, whereas the shear modulus and velocity are independent of it. Using the classical Gassmann model, the bulk moduli at different CO 2 saturations obtained from the data exceed the Gassmann-Voigt upper bound, which is attributed to elastic stiffening. To model the P-wave velocity and attenuation, we use a poroelastic (mesoscopic-loss) model with a fractal distribution of the radius of the CO 2 patches, and find that this model performs better than the White model, which is based on a single radius.