Analysis of pressure diffusion-wave fields in matrix-fracture media using Green functions of frequency domain

Abstract

A Green function-based analytic solution of pressure diffusive wave motion is introduced for investigating the transient pressure response in fluid saturated matrix-fracture media. One-dimensional solutions are presented for a time-harmonically forced problem with internal damping and are used to analyze the propagation and attenuation of pressure pulse in a semi-infinite spatial domain. The concise form of the solutions simplifies the calculation of pressure diffusion with arbitrary forcing functions at fixed boundaries. It indicates that the periodically forced function with internal damping has remarkable effects on pressure diffusion-wave motions. It is found that the characteristic delay-frequency separates the pressure diffusion-wave domain into matrix-dominated, transition, and fracture-dominated zones. The Green functions could physically predict any transient response of pressure fluctuations due to hydro-fracturing in geological reservoirs given proper physical parameters.