A VISCOELASTIC REPRESENTATION OF SEISMIC WAVE ATTENUATION AND DISPERSION CAUSED BY WAVE-INDUCED FLUID FLOW IN FRACTURED POROUS MEDIA

摘要

Analyzing and understanding the seismic response from fractured reservoirs is vital to reservoirs characterization and the production optimization of hydrocarbons. Fractured reservoirs can be modeled as fractured porous media. When seismic waves propagate in fractured porous media, fluid exchange occurs between the fractures and the pore space. As a consequence, the seismic waves are subject to attenuation and dispersion, the media behave viscoelasticity, and the components of the effective stiffness tensor involved in the stress-strain relation become complex-valued and frequency dependent. In order to compute synthetic seismograms in the time domain with the purpose of studying seismic response of the media, an efficient approach is to approximate the stiffnesses by suitable viscoelastic models and then solve viscoelastic differential equations. In this paper, based on the Chapman's model of fractured porous media, we use the Zener model to approximate each component of the effective stiffness tensor, and use the Christoffel equation to obtain the seismic attenuation and velocity dispersion curves and their corresponding Zener model best fits. We focused on three models, each with two different fracture sizes and filled with different fluids. Our results indicate that the Zener model provides a good representation for Chapman's model of fractured porous media.