An Assessment of the Effect of Capillary Pressure Changes on Dilatational Wave Propagation and Attenuation through Unsaturated Poroelastic Media

• Main Authors: Jhe-wei Li, 李哲瑋
• Other Authors: Wei-cheng Lo
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/83070672246980899695

碩士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 96 === Capillary pressure plays an important role in the description of the two-phase fluid flows in unsaturated porous media. In literature studies, a prevalent argument states that the effect of changes in capillary pressure can be ignored when the dilatational wave undergoes low-frequency motions because the wave excitation is of long enough wavelength that two immiscible pore fluids experience the same pressure. Therefore, the main objective of this study is to investigate the effect of capillary pressure changes on dilatational wave propagation and attenuation through unsaturated poroelastic media. We begin by driving a dispersion relation for the eigenvalues of two free dilatational modes from the Berryman et al. [1988] model, where capillary pressure changes are considered to be negligible due to the low-frequency assumption. Thus, we can predict the phase speed and attenuation coefficient of the fastest (P1) and second fastest (P2) dilatational waves from this relation and compare with Lo et al. [2005] model, in which capillary pressure effects are rigorously taken into account. As an illustrative example, Columbia fine sandy loan permeated by either an air-water or oil-water mixture was examined as functions of relative fluid saturation and wave excitation frequency (10 Hz, 1 kHz, and 100 kHz). Regardless of an air-water or oil-water mixture, our numerical results show that in the low-frequency range, the phase speed and attenuation coefficient of the P1 and P2 waves are not substantially affected by capillary pressure changes, which confirms the physical assumption typically made in literature studies. When dilatational wave undergoes high-frequency (100 kHz) motions, there are still no noticeable differences between the two models. However, a sensitivity analysis reveals that if the magnitude of changes of capillary pressure is greater, they indeed give an influence on the phase speed and attenuation coefficient of the P1 and P2 waves.