Elastic properties of fractures in transversely isotropic media

A fracture may be characterized by its normal and shear compliances that relate the discontinuity in displacement of the fracture faces to an applied traction. To assess the feasibility of using elastic waves for monitoring natural and hydraulic fractures in anisotropic shale reservoirs, an understanding of how these compliances relate to the properties of the background rock and any fracture infill material is required. Three models of vertical fractures in a VTI (transversely isotropic medium with vertical axis of rotational symmetry) background suitable for feasibility studies are discussed. The first two models are suitable for open vertical fractures and represent the fractures as aligned low aspect ratio elliptic cylindrical inclusions with long axis of the ellipse either horizontal or vertical. In these models the horizontal and vertical shear compliance differ in a way that depends on the anisotropy of the background medium and the orientation of the fractures. The third model is suitable for estimating the properties of hydraulic fractures containing proppant. In this model, proppant is represented as a random packing of identical elastic spheres subject to a uniaxial compression due to the normal stress acting on the fracture. The results are expected to help improve the reliability of fracture models used for assessing the feasibility of elastic waves for characterizing natural and hydraulic fractures.