Abstract:

Based on the anisotropic effective model of fracture medium, the authors analyzed velocities of compressional and shear waves, the variations of elastic stiffness modulus with respect to the fracture density, the fracture aspect ratio and the fluid properties filled in the pore. We also examined the applicability and the accuracy of Hudson model and its Pade approximation and the Liu fracture model, and focused on the effects on elastic modulus and velocities of the compressional and shear waves of the geometric parameters of the fracture pore, fracture porosity and the fluid filled in it. On the basis of the Pade approximation of Hudson fracture model, we proved that Pade approximation is suitable for higher fracture density and larger fracture aspect. The simulation results indicate that when the fracture density is less than 0.1,the Liu fracture model and Hudson second order approximation lead to consistent elastic response; Liu fracture model and Pade approximation are applicable to the cases when fracture density is less than 0.2; for the cases of fracture density larger than 0.2, the Liu model shows more reasonable result. Furthermore, in the water saturated and the dry fracture medium, the fracture aspect presents more significant effects on the the Liu model.

Key words: fracture, anisotropic effective medium, aspect ratio, density, fluid filled in fracture porosity, compressive and shear wave velocities, elastic stiffness modulus