Abstract
Taking into account three important porous media mechanisms during wave propagation (the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms), we introduce water saturation into the dynamic governing equations of wave propagation by analyzing the effective medium theory and then providing a viscoelastic Biot/squirt (BISQ) model which can analyze the wave propagation problems in a partially viscous pore fluid saturated porous media. In this model, the effects of pore fluid distribution patterns on the effective bulk modulus at different frequencies are considered. Then we derive the wave dynamic equations in the time-space domain. The phase velocity and the attenuation coefficient equations of the viscoelatic BISQ model in the frequency-wavenumber domain are deduced through a set of plane harmonic solution assumptions. Finally, by means of numerical simulations, we investigate the effects of water saturation, permeability, and frequency on compressional wave velocity and attenuation. Based on tight sandstone and carbonate experimental observed data, the compressional wave velocities of partially saturated reservoir rocks are calculated. The compressional wave velocity in carbonate reservoirs is more sensitive to gas saturation than in sandstone reservoirs.
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This work was jointly supported by the National Natural Science Foundation of China (No. 11002025, 40114066), the National Basic Research Program of China (973 Program) (No.2007CB209505), and the RIPED Youth Innovation Foundation (No. 2010-A-26-01).
Nie Jian-Xin: See biography and photo in the Applied Geophysics December 2008 issue, P. 260.
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Nie, JX., Ba, J., Yang, DH. et al. BISQ model based on a Kelvin-Voigt viscoelastic frame in a partially saturated porous medium. Appl. Geophys. 9, 213–222 (2012). https://doi.org/10.1007/s11770-012-0332-6
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DOI: https://doi.org/10.1007/s11770-012-0332-6