Influence of Fracture Geometry on the Krauklis Wave in Finite Fractures

Abstract

Study of the Krauklis wave in fractured media reveals the potential for characterizing fracture geometry. In this paper, a finite element scheme is proposed to simulate the Krauklis wave in fractures with different geometries. The influence of fracture geometry on the propagation properties of the Krauklis waves is evaluated. Here, fracture geometry refers to the fracture shape, width, and length. First, a series of numerical models containing a single water-filled fracture is set up, in which the fracture shape can be an ellipse or rectangle, its width varies from 5 to 10 mm, and its length varies from 2 to 3 m. The proposed finite element scheme is applied to simulate Krauklis waves. From these simulation results, the Krauklis wave signals inside the fractures are extracted, and a velocity estimation method is developed and implemented to estimate the average velocity within the finite length fractures. For comparison, the theoretical velocity is solved from a dispersion equation, in which the fracture is assumed to be an infinite thin fluid layer. It is shown that the rectangular fractures generate stronger amplitude and higher velocity waves than the elliptical ones. The amplitude varies along the fracture and can be significantly affected by the fracture geometry. Furthermore, the velocity increases with the fracture width, whereas the fracture length does not affect the velocity for both elliptical and rectangular fractures. These effects indicate that Kraulklis waves are rich in information about fracture geometry, and this is valuable when applied to the quantitative characterization of fractures.