Effects of randomly orienting penny-shaped cracks on the elastic properties of transversely isotropic rocks

Fractured reservoirs, as one kind of unconventional reservoirs, have great potential for oil and gas development, and their accurate characterization requires the development of rock physics models that better simulate real fractured rocks. However, current models focus mainly on the elastic properties of rocks with aligned cracks, while the effects of randomly orienting cracks in transversely isotropic (TI) rocks are poorly studied even though such conditions are frequently encountered in the earth. To address this problem, we have derived models for the elastic properties of rocks with a TI background permeated by 3D inclined cracks and randomly orienting cracks. Then, based on the developed models, we comprehensively study the effects of the two inclination angles (i.e., the dip angle between the cracks and the isotropic plane and the rotation angle between the cracks and the plane normal to the isotropic plane, respectively) of 3D inclined cracks on the elastic properties of TI rocks. We determine that the two angles have significant influences on the elastic coefficients and hence the elastic velocities, and that their influences on the elastic properties are varying in different directions. We further investigate the effects of crack density and aspect ratio of randomly orienting cracks on the elastic properties of the fractured rocks with a TI background. The results show that the increasing crack density and crack aspect ratio reduce the elastic coefficients and velocities for rocks with randomly orienting cracks, in which the relations between compressional-wave velocities and the crack properties (i.e., crack density and crack aspect ratio) are obtained to aid the interpretation of the acquired acoustic exploration data. The proposed new models can greatly improve the modeling capability for the elastic properties of rocks with a TI background permeated by inclined and randomly orienting cracks.