Full Solutions for Reflection and Conversion Coefficients at a Thin Fluid Layer Representing a Hydraulic Fracture

Abstract

Understanding the properties of hydraulic fractures, for example their growth mechanism, is a main task in their investigation. We model a hydraulic fracture by a thin layer of an ideal fluid which is embedded between an elastic and isotropic solid with identical properties on each side of the crack. The main goal of this work is to find reflection coefficients for a wave reflected at this thin fluid layer. We present full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, the S-S and S-P reflection coefficients. We find that for parameters in the range of microseismic needs, which means a layer thickness of h=0.001-0.01m and frequencies of f=50-400Hz, the reflection coefficients change with Poisson's ratio. Furthermore the reflections of an incident S-wave are significantly high. This allows us to image hydraulic fractures using microseismic events as a source. The results presented in this paper will help to understand the properties of hydraulic fractures and can be used to characterize reservoirs or improve the imaging of hydraulic fractures.