Coupled waves at fracture intersections
Abstract:Fracture intersections play a crucial role in the hydraulic connectivity of flow paths in rock, yet no current techniques exist for characterizing the conditions of an intersection. We demonstrate experimentally and theoretically that elastic waves propagated along fracture intersections are affected by the amount of contact among the blocks forming an intersection.
Surface fractures and fracture intersections can be viewed as wedges (corners) coupled through the points of contact along the intersection. An eigenvalue secular equation was derived using displacement discontinuity theory along with the solution for a wedge wave. The velocity and motion of intersection waves are a function of the frequency, material impedance, and specific stiffness of the intersection. For an intersection, several modes are present that represent the coupling between different sets of the wedges and exhibit wave speeds between a single wedge mode and the bulk S wave. A surface fracture supports only one mode of propagation with speeds that range from the single wedge wave to that of the Rayleigh wave.
Experiments were performed on intersections made from two or four aluminum samples (0.29 x 0.076 x 0.076 m) to detect intersection waves. Measurements were made under uniaxial and biaxial loading conditions to change the contact area along an intersection. At low loads both the surface fracture and intersection excite wedge waves because the stress between the wedges was not sufficiently high to couple the wedges. As the external load was increased, the wave coupled the wedges and propagated as a Rayleigh wave for the surface fracture, or as a bulk S wave for the intersection. These results indicate that the specific stiffness of the fracture intersection can be estimated based upon the velocity of the wave propagating along the intersection or surface fracture. Using this estimation the flow path(s) along or through the fracture intersection or surface fracture can be characterized and used as a tool to determine which flow path is most likely for a given sample.
Acknowledgments: This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Geo-sciences Research Program under Award Number (DE-FG02-09ER16022) and by the Geo-Mathematical Imaging Group at Purdue