The modeling and analysis of frequency-dependent characteristics in fractured porous media

Abstract

At present, most studies have considered partial saturation and aligned fractures separately. However, these two phenomena exist simultaneously in most fractured reservoirs, such as carbonate reservoirs and tight sandstone reservoirs. In this paper, we develop a periodically layered model with alternating fractured layer saturated with gas and water-bearing porous layer to simultaneously model partial saturation and aligned fractures, which is an equivalent viscoelastic vertical transversely isotropic medium. We assume that the two types of attenuation are independent of each other. Firstly, we analyze the phase velocities and attenuation coefficients of quasi-P (P) and quasi-S (S) waves with frequency and incident angle, when the thickness fraction of fractured layer is 0.5. It shows that the attenuation coefficients of P-wave are much greater than the S-wave, when the incident angle is smaller than 30°. Then we analyze the frequency-dependent characteristics of the P-wave with different thickness of the fractured layer related to gas saturation. The attenuation of P-wave increases significantly with gas saturation in the frequency band from 10 to 100 Hz. Finally, we re-derived the frequency-dependent amplitude versus offset equation of anisotropic media to analyze the dispersion characteristics of the P-wave reflection coefficients. The reflection magnitude decreases with frequency and the reflection coefficients show significant anisotropy at high gas saturation. The dispersion and attenuation of P-wave largely depends on the gas saturation.